Operator Theory: Advances and Applications

Founded in 1979 by Israel Gohberg

Volume 259

Joseph A. Ball (Blacksburg, VA, USA) Harry Dym (Rehovot, Israel) Marinus A. Kaashoek (Amsterdam, The Netherlands) Heinz Langer (Wien, Austria) Christiane Tretter (Bern, Switzerland)

Vadim Adamyan (Odessa, Ukraine)

Albrecht Böttcher (Chemnitz, Germany) B. Malcolm Brown (Cardiff, UK) Raul Curto (Iowa, IA, USA) Fritz Gesztesy (Columbia, MO, USA) Pavel Kurasov (Stockholm, Sweden)

Lewis A. Coburn (Buffalo, NY, USA) Ciprian Foias (College Station, TX, USA) J.William Helton (San Diego, CA, USA) Thomas Kailath (Stanford, CA, USA) Peter Lancaster (Calgary, Canada) Peter D. Lax (New York, NY, USA) Donald Sarason (Berkeley, CA, USA) Bernd Silbermann (Chemnitz, Germany) Harold Widom (Santa Cruz, CA, USA)

Associate Editors: Honorary and Advisory Editorial Board:

Editors:

Wolfgang Arendt (Ulm, Germany)

Vern Paulsen (Houston, TX, USA) Mihai Putinar (Santa Barbara, CA, USA)

Subseries Linear Operators and Linear Systems Subseries editors: Daniel Alpay (Orange, CA, USA) Birgit Jacob (Wuppertal, Germany) André C.M. Ran (Amsterdam, The Netherlands) Subseries Advances in Partial Differential Equations Subseries editors: Bert-Wolfgang Schulze (Potsdam, Germany) Michael Demuth (Clausthal, Germany) Jerome A. Goldstein (Memphis, TN, USA) Nobuyuki Tose (Yokohama, Japan) Ingo Witt (Göttingen, Germany)

More information about this series at http://www.springer.com/series/4850

Ilya Spitkovsky (Abu Dhabi, UAE)

Editors

Dario A. Bini • Torsten Ehrhardt Alexei Yu. Karlovich • Ilya Spitkovsky

Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics The Albrecht Böttcher Anniversary Volume

EditorsDario A. Bini Torsten Ehrhardt Dipartimento di Matematica Mathematics Department Università di Pisa University of California Pisa, Italy Santa Cruz, California, USA

Alexei Yu. Karlovich Ilya Spitkovsky Departamento de Matemática New York University Abu Dhabi

Caparica, Portugal

Abu Dhabi, United Arab Emirates

(electronic)

(eBook)

Library of Congress Control Number:

© Springer International Publishing AG 2017

ISSN 2296-4878 Operator Theory: Advances and Applications ISSN 0255-0156

ISBN 978-3-319-49180-6 ISBN 978-3-319-49182-0 DOI 10.1007/978-3-319-49182-0

Mathematics Subject Classification (2010): 15B05, 47B35, 60B20

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Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

Publications of Albrecht Bottcher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

S. GrudskyAlbrecht Bottcher – 20 Years of Friendship and Joint Work . . . . . . . . . 1

J. JahnsSalutatory with Regards from the MathematicsStudents of Chemnitz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

B. SilbermannEssay on Albrecht Bottcher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

F.-O. SpeckMeeting Albrecht the Strong . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

I. SpitkovskyThe Beginning (the Way I Remember it) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

D. WenzelPersonal Address on the Occasion of Albrecht Bottcher’s60th Birthday . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

M. Barrera and S.M. GrudskyAsymptotics of Eigenvalues for Pentadiagonal SymmetricToeplitz Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

H. Bart, T. Ehrhardt and B. SilbermannEchelon Type Canonical Forms in Upper TriangularMatrix Algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

E. Basor and T. EhrhardtAsymptotic Formulas for Determinants of a Special Class ofToeplitz + Hankel Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

vi Contents

D.A. Bini and B. MeiniGeneralization of the Brauer Theorem to Matrix Polynomialsand Matrix Laurent Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

J.M. Bogoya, S.M. Grudsky and E.A. MaximenkoEigenvalues of Hermitian Toeplitz Matrices Generated bySimple-loop Symbols with Relaxed Smoothness . . . . . . . . . . . . . . . . . . . . . 179

T. Bothner, P. Deift, A. Its and I. KrasovskyOn the Asymptotic Behavior of a Log Gas in the Bulk ScalingLimit in the Presence of a Varying External Potential II . . . . . . . . . . . . . 213

D. Bump, P. Diaconis, A. Hicks, L. Miclo and H. WidomUseful Bounds on the Extreme Eigenvalues and Vectors ofMatrices for Harper’s Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235

T. Ehrhardt and K. RostFast Inversion of Centrosymmetric Toeplitz-plus-HankelBezoutians . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267

B. Fritzsche, B. Kirstein and C. MadlerOn Matrix-valued Stieltjes Functions with an Emphasis onParticular Subclasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301

C. Garoni and S. Serra-CapizzanoThe Theory of Generalized Locally Toeplitz Sequences:a Review, an Extension, and a Few Representative Applications . . . . . 353

G.J. Groenewald, S. ter Horst and M.A. KaashoekThe Bezout Equation on the Right Half-plane in a WienerSpace Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

P. Junghanns and R. KaiserOn a Collocation-quadrature Method for the Singular IntegralEquation of the Notched Half-plane Problem . . . . . . . . . . . . . . . . . . . . . . . . 413

Yu.I. KarlovichThe Haseman Boundary Value Problem with Slowly OscillatingCoefficients and Shifts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463

N. Krupnik and A. MarkusOn the Norm of Linear Combinations of Projections and SomeCharacterizations of Hilbert Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501

V. Kryakvin and V. RabinovichPseudodifferential Operators in Weighted Holder–ZygmundSpaces of Variable Smoothness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511

Contents vii

Z. Lu and D. WenzelCommutator Estimates Comprising the Frobenius Norm –Looking Back and Forth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533

E. Militzer, L.J. Patton, I.M. Spitkovsky and M.-C. TsaiNumerical Ranges of 4-by-4 Nilpotent Matrices: Flat Portionson the Boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561

A. PietschTraces on Operator Ideals and Related Linear Forms on SequenceIdeals (Part IV) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593

D. Potts and M. TascheError Estimates for the ESPRIT Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 621

S. RochThe Universal Algebra Generated by a Power Partial Isometry . . . . . . 649

M. SeidelNorms, Condition Numbers and Pseudospectra of ConvolutionType Operators on Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663

F.-O. SpeckPaired Operators in Asymmetric Space Setting . . . . . . . . . . . . . . . . . . . . . . 681

C.A. Tracy and H. WidomNatural Boundary for a Sum Involving Toeplitz Determinants . . . . . . . 703

E. WegertA Riemann–Hilbert Approach to Filter Design . . . . . . . . . . . . . . . . . . . . . . 719

Preface

This volume is dedicated to Albrecht Bottcher on the occasion of his sixtiethbirthday. The first part contains two essays written by Sergei Grudsky and BerndSilbermann, and several personal recollections written by colleagues, students, andfriends of Albrecht. The second part consists of twenty four selected scientific pa-pers devoted to various fields of Analysis andMatrix Theory, including asymptoticsof Toeplitz and Hankel matrices, boundary value problems and singular integraloperators, numerical ranges and pseudospectra, convolution and pseudodifferen-tial operators. Albrecht Bottcher has been enriching all these areas by fundamentalcontributions during more than three decades. The volume ends with the contri-bution by Elias Wegert, who was a classmate of Albrecht in “Spezialklasse furMathematik und Physik, Hochschule Karl-Marx-Stadt”. It tells us about the firststeps of in Mathematics. We thank all contributors forwhen preparing the articles for this volume. We feel happy toBottcher by the edition of this volume, and wish him good healthsuccess in his work.

September 2016 Dario A. Bini,Torsten Ehrhardt,Alexei Yu. Karlovich,Ilya Spitkovsky

Albrecht their enthusiasmhonour Albrechtand ever greater

Albrecht Bottcher

Operator Theory:Advances and Applications, Vol. 259, xi–xxvic© 2017 Springer International Publishing

Publications of Albrecht Bottcher

Books

1. A. Bottcher and B. Silbermann: Invertibility and Asymptotics of ToeplitzMatrices. Mathematical Research, Vol. 17. Akademie-Verlag, Berlin, 1983.

2. A. Bottcher and B. Silbermann: Analysis of Toeplitz Operators. Akademie-Verlag, Berlin, 1989 and Springer-Verlag, Berlin, Heidelberg, New York, 1990(1st edition).

3. A. Bottcher, A. Dijksma, H. Langer, M.A. Dritschel, J. Rovnyak, and M.A.Kaashoek: Lectures on Operator Theory and Its Applications. Fields InstituteMonographs, Vol. 3. Edited by Peter Lancaster. American Mathematical So-ciety, Providence, RI, 1996.

4. A. Bottcher and Yu.I. Karlovich: Carleson Curves, Muckenhoupt Weights,and Toeplitz Operators. Progress in Mathematics, Vol. 154. Birkhauser Ver-lag, Basel, 1997.

5. A. Bottcher and B. Silbermann: Introduction to Large Truncated ToeplitzMatrices. Universitext, Springer-Verlag, New York, 1999.

6. A. Bottcher and S. Grudsky: Toeplitz Matrices, Asymptotic Linear Algebra,and Functional Analysis. Texts and Readings in Mathematics, Vol. 18. Hin-dustan Book Agency, New Delhi, 2000 and Birkhauser Verlag, Basel, 2000.

7. A. Bottcher, Yu.I. Karlovich, and I.M. Spitkovsky: Convolution Operatorsand Factorization of Almost Periodic Matrix Functions. Operator Theory:Advances and Applications, Vol. 131. Birkhauser Verlag, Basel, 2002.

8. A. Bottcher and S.M. Grudsky: Spectral Properties of Banded Toeplitz Ma-trices. SIAM, Philadelphia, 2005.

9. A. Bottcher and B. Silbermann: Analysis of Toeplitz Operators. Springer-Verlag, Berlin, Heidelberg, New York, 2006. (2nd edition).

xii Publications of Albrecht Bottcher

Papers

1. A. Bottcher and B. Silbermann: Notes on the asymptotic behavior of blockToeplitz matrices and determinants. Math. Nachr. 98 (1980), 183–210.

2. A. Bottcher and B. Silbermann: The asymptotic behavior of Toeplitz deter-minants for generating functions with zeros of integral orders. Math. Nachr.102 (1981), 79–105.

3. A. Bottcher and B. Silbermann: Uber das Reduktionsverfahren fur diskreteWiener–Hopf-Gleichungen mit unstetigem Symbol. Z. Analysis Anw. 1 (1982),1–5.

4. A. Bottcher: Toeplitz determinants with piecewise continuous generating func-tion. Z. Analysis Anw. 1 (1982), 23–39.

5. A. Bottcher and A.E. Pasenchuk: On the invertibility of Wiener–Hopf oper-ators on the quarter-plane. In: Differential and Integral Equations, pp. 9–19,Elista, 1982 (in Russian).

6. A. Bottcher: On two-dimensional Wiener–Hopf integral equations with a de-generate symbol. Math. Nachr. 109 (1982), 195–213 (in Russian).

7. A. Bottcher: Toeplitzdeterminanten in der statistischen Physik. In: Ergebnissed. Schule Junger Wissenschaftler zur Math. Physik, pp. 19–21, Pruchten,1982.

8. A. Bottcher and B. Silbermann: Wiener–Hopf determinants with symbolshaving zeros of analytic type. Seminar Analysis 1982/83 (1983), 224–243.

9. A. Bottcher and B. Silbermann: The finite section method for Toeplitz oper-ators on the quarter-plane with piecewise continuous symbols. Math. Nachr.110 (1983), 279–291.

10. A. Bottcher: Two-dimensional convolutions in angles with kernels supportedin a half-plane. Matem. Zametki 34 (1983), 207–218 (in Russian). Engl.transl. in Math. Notes 34 (1983), 585–591.

11. A. Bottcher: Fredholm theory and finite section method for two-dimensionalWiener–Hopf operators with piecewise continuous symbols. Dokl. Akad. NaukSSSR 273 (1983), 1298–1300 (in Russian). Engl. transl. in Soviet Math. Dokl.28 (1983), 773–776.

12. A. Bottcher: Das Reduktionsverfahren fur nichtelliptische Wiener–Hopf’scheIntegraloperatoren in einer Klasse von topologischen Vektorraumen. Wiss.Zeitschr. TH Karl-Marx-Stadt 25 (1983), 308–312.

13. A. Bottcher: Fredholmness and finite section method for Toeplitz operators in�p(Z+ × Z+). Z. Analysis Anw. 3 (1984), 97–110.

14. A. Bottcher: Fredholmness and finite section method for Toeplitz operators in�p(Z+ × Z+), II. Z. Analysis Anw. 3 (1984), 191–202.

15. A. Bottcher: The finite section method for Wiener–Hopf integral operatorswith piecewise continuous symbols in the spaces Lp. Funkts. Anal. Prilozh.

Publications of Albrecht Bottcher xiii

18 (1984), 55–56 (in Russian). Engl. transl. in Funct. Anal. Appl. 18 (1984),132–133.

16. A. Bottcher: The finite section method for two-dimensional Wiener–Hopf op-erators in Lp with piecewise continuous symbols. Math. Nachr. 116 (1984),61–73.

17. A. Bottcher and B. Silbermann: Toeplitz determinants with symbols from theFisher–Hartwig class. Dokl. Akad. Nauk SSSR 278 (1984), 13–16 (in Russian).Engl. transl. in Soviet Math. Dokl. 30 (1984), 301–304.

18. A. Bottcher and B. Silbermann: Toeplitz determinants generated by symbolswith one singularity of Fisher–Hartwig type. Wiss. Zeitschr. TH Karl-Marx-Stadt 26 (1984), 186–188.

19. A. Bottcher and B. Silbermann: Toeplitz matrices and determinants withFisher–Hartwig symbols. J. Funct. Analysis 63 (1985), 178–214.

20. A. Bottcher: Scalar Toeplitz operators, distance estimates, and localizationover subalgebras of C +H∞. Seminar Analysis 1985/1986 (1986), 1–17.

21. A. Bottcher: A remark on the relation between the partial indices of a matrixfunction and its harmonic extension. Seminar Analysis 1985/86 (1986), 19–22.

22. A. Bottcher, S. Roch, and B. Silbermann: Local constructions and Banachalgebras associated with Toeplitz operators on Hp. Seminar Analysis 1985/86(1986), 23–30.

23. A. Bottcher and B. Silbermann: Toeplitz operators and determinants gen-erated by symbols with one Fisher–Hartwig singularity. Math. Nachr. 127(1986), 95–124.

24. A. Bottcher: On Toeplitz operators generated by symbols with three essentialcluster points. Preprint P-Math-04/86, 22 pages, Karl-Weierstrass-Institut,Berlin 1986 (never published but often cited).

25. A. Bottcher and B. Silbermann: Local spectra of approximate identities, clus-ter sets, and Toeplitz operators. Wiss. Zeitschr. TH Karl-Marx-Stadt 28(1986), 175–180.

26. A. Bottcher: Multidimensional Toeplitz operators with locally sectorial sym-bols. Seminar Analysis 1986/87 (1987), 1–16.

27. A. Bottcher and B. Silbermann: Toeplitz operators with symbols from C+H∞

in the spaces �p. Zap. Nauchn. Sem. LOMI 157 (1987), 124–128 (in Russian).Engl. transl. in J. Soviet Math. 44 (1989), 834–836.

28. A. Bottcher: Asymptotic formulas for rationally generated block Toeplitz de-terminants. Seminar Analysis 1987/88 (1988), 1–13.

29. A. Bottcher and B. Silbermann: Asymptotics of Toeplitz and Wiener–Hopfoperators. In: Proc. 9th Conf. Probl. and Meth. in Math. Phys., Karl-Marx-Stadt 1988, pp. 27–35, Teubner, 1988.

xiv Publications of Albrecht Bottcher

30. A. Bottcher, N. Krupnik, and B. Silbermann: A general look at local principleswith special emphasis on the norm computation aspect. Integral Equationsand Operator Theory 11 (1988), 455–479.

31. A. Bottcher and S. Dzhirgalova: On Wiener–Hopf determinants with rationalmatrix symbols. Seminar Analysis 1988/89 (1989), 21–39.

32. A. Bottcher: On Mikaelyan’s conjecture in the theory of Wiener–Hopf de-terminants. Izv. Armen. Akad. Nauk 24 (1989), 188–192 (in Russian). Engl.transl. in Sov. J. Contemp. Math. Anal., Arm. Acad. Sci. 24 (1989), 85–89.

33. A. Bottcher: Wiener–Hopf determinants with rational symbols. Math. Nachr.144 (1989), 39–64.

34. A. Bottcher: Status report on rationally generated block Toeplitz and Wiener–Hopf determinants. Unpublished manuscript (available from the author onrequest), 1989.

35. A. Bottcher and H. Heidler: On linear functional equations with two involu-tions. Seminar Analysis 1989/90 (1990), 31–43.

36. A. Bottcher: Truncated Toeplitz operators on the polydisk. Monatshefte f.Math. 110 (1990), 23–32.

37. A. Bottcher, B. Silbermann, and I. Spitkovsky: Toeplitz operators with piece-wise quasisectorial symbols. Bull. London Math. Soc. 22 (1990), 281–286.

38. A. Bottcher, S. Roch, B. Silbermann, and I. Spitkovsky: A Gohberg–Krupnik–Sarason symbol calculus for algebras of Toeplitz, Hankel, Cauchy, and Carle-man operators. Operator Theory: Adv. and Appl. 48 (1990), 189–234.

39. A. Bottcher and I. Spitkovsky: Toeplitz operators with PQC symbols onweighted Hardy spaces. J. Funct. Analysis 97 (1991), 194–214.

40. A. Bottcher and H. Wolf: Finite sections of Segal–Bargmann space Toeplitzoperators with polyradially continuous symbols. Bull. Amer. Math. Soc. 25(1991), 365–372.

41. A. Bottcher: Invertible values of elementary operators and projection methodsfor Toeplitz operators. In: Proc. Internat. Conf. on Elementary Operators,Blaubeuren 1991, pp. 157–161, World Scientific Publishing Co., Singapore,1992.

42. A. Bottcher and H. Wolf: Large sections of Bergman space Toeplitz operatorswith piecewise continuous symbols. Math. Nachr. 156 (1992), 129–155.

43. A. Bottcher and H. Wolf: Collocation methods for Toeplitz operators onDzhrbashyan spaces. Bull. Armen. Acad. Sci. 93 (1992), 168–172 (Russian).

44. A. Bottcher and H. Heidler: Algebraic composition operators. Integral Equa-tions and Operator Theory 15 (1992), 389–411.

45. A. Bottcher and H. Wolf: Interpolation in the Bergman space, mean valuesof harmonic functions, and an inverse problem of potential theory. Wiss. Z.TU Chemnitz 34 (1992), 31–35.

Publications of Albrecht Bottcher xv

46. A. Bottcher and I. Spitkovsky: Wiener–Hopf integral operators with PC sym-bols on spaces with Muckenhoupt weight. Revista Matematica Iberoamericana9 (1993), 257–279.

47. A. Bottcher and H. Wolf: Galerkin–Petrov methods for Bergman spaceToeplitz operators. SIAM J. Numer. Analysis 30 (1993), 846–863.

48. A. Bottcher and I. Spitkovsky: On a theorem of Rooney concerning the spec-trum of the singular integral operator. Z. Analysis Anw. 12 (1993), 93–96.

49. A. Bottcher: Toeplitz operators on the disk with locally sectorial symbols.Rocky Mountain J. Math. 23 (1993), 803–816.

50. A. Bottcher and H. Heidler: Classification of finite-dimensional algebras gen-erated by the Calkin image of a composition operator on �p with weight. Alge-bra i Analiz 5 (1993), 69–96 and St. Petersburg Math. J. 5 (1994), 1099–1119.

51. A. Bottcher and B. Silbermann: Axler–Chang–Sarason–Volberg theorems forharmonic approximation and stable convergence. In: Linear and ComplexAnalysis Problem Book 3, Part I (V.P. Havin, N.K. Nikolski, eds.), pp. 340–341, Lecture Notes in Math., Vol. 1573, Springer-Verlag, 1994.

52. A. Bottcher and H. Wolf: Asymptotic invertibility of Bergman and Bargmannspace Toeplitz operators. Asymptotic Analysis 8 (1994), 15–33.

53. A. Bottcher: Magnete, Determinanten und Fourier-Summen. Spektrum derWissenschaft 3/1994 (1994), 25–27.

54. A. Bottcher, Yu.I. Karlovich, and B. Silbermann: Singular integral operatorswith PQC coefficients and freely transformed argument. Math. Nachr. 166(1994), 113–133.

55. A. Bottcher, Yu.I. Karlovich, and I. Spitkovsky: Toeplitz operators with semi-almost periodic symbols on spaces with Muckenhoupt weight. Integral Equa-tions and Operator Theory 18 (1994), 261–276.

56. A. Bottcher and H. Widom: Two remarks on spectral approximations forWiener–Hopf operators. J. Integral Equations Appl. 6 (1994), 31–36.

57. A. Bottcher and B. Silbermann: Operator-valued Szego–Widom limit theo-rems. Operator Theory: Adv. and Appl. 71 (1994), 33–53.

58. A. Bottcher, B. Silbermann, and H. Widom: A continuous analogue of theFisher–Hartwig formula for piecewise continuous symbols. J. Funct. Analysis122 (1994), 222–246.

59. A. Bottcher, B. Silbermann, and H. Widom: Determinants of truncated Wie-ner–Hopf operators with Hilbert–Schmidt kernels and piecewise continuoussymbols. Archiv d. Math. 63 (1994), 60–71.

60. A. Bottcher and I. Spitkovsky: Pseudodifferential operators with heavy spec-trum. Integral Equations and Operator Theory 19 (1994), 251–269.

61. A. Bottcher: Pseudospectra and singular values of large convolution operators.J. Integral Equations Appl. 6 (1994), 267–301.

xvi Publications of Albrecht Bottcher

62. A. Bottcher: The Onsager formula, the Fisher–Hartwig conjecture, and theirinfluence on research into Toeplitz operators. J. Statistical Physics 78 (LarsOnsager Festschrift) (1995), 575–585.

63. A. Bottcher and H. Wolf: Analytic element collocation over geodesic circlesfor Bergman space Toeplitz operators. In: Proc. Internat. Conf. DifferentialGeometry, Hamiltonian Systems, and Operator Theory, Kingston, Jamaica,1994, pp. 69–87, University of the West Indies Press, Mona, 1995.

64. A. Bottcher and H. Heidler: Algebraic and essentially algebraic compositionoperators on C(X). Aequationes Mathematicae 49 (1995), 276–294.

65. A. Bottcher and Yu.I. Karlovich: Toeplitz and singular integral operators onCarleson curves with logarithmic whirl points. Integral Equations and Oper-ator Theory 22 (1995), 127–161.

66. A. Bottcher: Toeplitz operators with piecewise continuous symbols – a nev-erending story? Jahresbericht der DMV 97 (1995), 115–129.

67. A. Bottcher and B. Silbermann: Infinite Toeplitz and Hankel matrices withoperator-valued symbols. SIAM J. Math. Analysis 27 (1996), 805–822.

68. A. Bottcher and H. Wolf: Polynomial collocation over massive sets for Toeplitzintegral equations on the Bergman space. J. Computational and AppliedMath. 66 (1996), 89–96.

69. A. Bottcher and Yu.I. Karlovich: Submultiplicative functions and spectral the-ory of Toeplitz operators. Integral Transforms and Special Functions 4 (1996),181–202.

70. A. Bottcher: Mathematischer Beweis versus Computerexperiment. In: Wiss.Kolloquium “Zum Nutzen von Grundlagenforschung”, Villa Hugel, 30. No-vember 1995, pp. 39–42, Krupp-Stiftung, Essen, 1996.

71. A. Bottcher, Yu.I. Karlovich, and V.S. Rabinovich: Emergence, persistence,and disappearance of logarithmic spirals in the spectra of singular integraloperators. Integral Equations and Operator Theory 25 (1996), 406–444.

72. A. Bottcher, I. Gohberg, Yu.I. Karlovich, N. Krupnik, S. Roch, B. Silber-mann, and I. Spitkovsky: Banach algebras generated by N idempotents andapplications. Operator Theory: Adv. and Appl. 90 (1996), 19–54.

73. A. Bottcher and S. Grudsky: Toeplitz operators with discontinuous symbols:phenomena beyond piecewise discontinuity. Operator Theory: Adv. and Appl.90 (1996), 55–118.

74. A. Bottcher and Yu.I. Karlovich: Toeplitz and singular integral operators ongeneral Carleson Jordan curves. Operator Theory: Adv. and Appl. 90 (1996),119–152.

75. A. Bottcher and H. Heidler: Characteristic polynomials of composition op-erators. In: Proc. European Conf. on Iteration Theory, Batschuns, Austria,1992, pp. 279–280, World Scientific Publishing Co., Singapore, 1996.

Publications of Albrecht Bottcher xvii

76. A. Bottcher: Infinite matrices and projection methods. In: Lectures on Opera-tor Theory and Its Applications (P. Lancaster, ed.), pp. 1–72, Fields InstituteMonographs, Vol. 3, Amer. Math. Soc., Providence, RI, 1996.

77. A. Bottcher: Review of “Spectral Theory of Approximation Methods for Con-volution Operators” by R. Hagen, S. Roch, and B. Silbermann. Bull. Amer.Math. Soc. 33 (1996), 237–243.

78. A. Bottcher and H. Wolf: Spectral approximation for Segal–Bargmann spaceToeplitz operators. In: Linear Operators, Banach Center Publ., Vol. 38, pp.25–48, PAN, Warsaw, 1997.

79. A. Bottcher and Yu.I. Karlovich: The algebra of singular integral operators onthe Lebesgue space on a closed Carleson curve. Dokl. Akad. Nauk 357 (1997),7–10 (in Russian). Engl. transl. in Doklady Math. 56 (1997), 813–816.

80. A. Bottcher, S. Grudsky, and B. Silbermann: Norms of inverses, spectra, andpseudospectra of large truncated Wiener–Hopf operators and Toeplitz matri-ces. New York J. Math. 3 (1997), 1–31.

81. A. Bottcher: On the approximation numbers of large Toeplitz matrices. Doc-umenta Mathematica 2 (1997), 1–29.

82. A. Bottcher and Yu.I. Karlovich: The algebra of singular integral operatorson a Lebesgue space with a Muckenhoupt weight on a closed Carleson curve.Dokl. Akad. Nauk 359 (1998), 151–154 (in Russian). Engl. transl. in DokladyMath. 57 (1998), 193–196.

83. A. Bottcher, Yu.I. Karlovich, and V.S. Rabinovich: Mellin pseudodifferen-tial operators with slowly varying symbols and singular integrals on Carlesoncurves with Muckenhoupt weights. Manuscripta Mathematica 95 (1998), 363–376.

84. A. Bottcher and S. Grudsky: On the condition numbers of large semi-definiteToeplitz matrices. Linear Algebra Appl. 279 (1998), 285–301.

85. A. Bottcher and S. Grudsky: On the composition of Muckenhoupt weightsand inner functions. J. London Math. Soc. 58 (1998), 172–184.

86. A. Bottcher: On the corona theorem for almost periodic functions. IntegralEquations and Operator Theory 33 (1999), 253–272.

87. A. Bottcher and Yu.I. Karlovich: Toeplitz operators with PC symbols ongeneral Carleson Jordan curves with arbitrary Muckenhoupt weights. Trans.Amer. Math. Soc. 351 (1999), 3143–3196.

88. C.J. Bishop, A. Bottcher, Yu.I. Karlovich, and I. Spitkovsky: Local spectraand index of singular integral operators with piecewise continuous coefficientson composed curves. Math. Nachr. 206 (1999), 5–83.

89. A. Bottcher and S. Grudsky: Toeplitz band matrices with exponentially grow-ing condition numbers. Electronic Journal of Linear Algebra (ELA) 5 (1999),104–125.

xviii Publications of Albrecht Bottcher

90. A. Bottcher, S. Grudsky, A. Kozak, and B. Silbermann: Norms of largeToeplitz band matrices. SIAM J. Matrix Analysis Appl. 21 (1999), 547–561.

91. A. Bottcher, S. Grudsky, A. Kozak, and B. Silbermann: Convergence speedestimates for the norms of the inverses of large truncated Toeplitz matrices.Calcolo 36 (1999), 103–122.

92. A. Bottcher and M. Seybold:Wackelsatz and Stechkin’s inequality for discreteMuckenhoupt weights. Preprint 99-7, 12 pages, TU Chemnitz, Fakultat furMathematik, Chemnitz 1999 (will not be submitted for publication; containsfull proofs to two basic theorems used in paper No. 98).

93. A. Bottcher and S. Grudsky: Eighteen old and new asymptotic results onToeplitz band matrices. In: Large-Scale Scientific Computations of Engineer-ing and Environmental Problems II (M. Griebel, S. Margenov, P. Yalamov,eds.), pp. 65–71, Vieweg, Braunschweig, 2000.

94. A. Bottcher, Yu.I. Karlovich, and V.S. Rabinovich: The method of limit op-erators for one-dimensional singular integrals with slowly oscillating data. J.Operator Theory 43 (2000), 171–198.

95. A. Bottcher, S. Grudsky, and I. Spitkovsky: On the Fredholm indices of as-sociated systems of Wiener–Hopf equations. J. Integral Equations Appl. 12(2000), 1–29.

96. A. Bottcher, S. Grudsky, and I. Spitkovsky: Matrix functions with arbitrar-ily prescribed left and right partial indices. Integral Equations and OperatorTheory 36 (2000), 71–91.

97. A. Bottcher, S. Grudsky, and I. Spitkovsky: The spectrum is discontinuouson the manifold of Toeplitz operators. Archiv d. Math. 75 (2000), 46–52.

98. A. Bottcher and M. Seybold: Discrete Wiener–Hopf operators on spaces withMuckenhoupt weight. Studia Math. 143 (2000), 121–144.

99. A. Bottcher: C∗-algebras in numerical analysis. Irish Math. Soc. Bulletin 45(2000), 57–133.

100. A. Bottcher and S. Grudsky: Twenty old and new asymptotic results onToeplitz band matrices. In: Structured Matrices: Recent Developments inTheory and Computation (D.A. Bini, E. Tyrtyshnikov, P. Yalamov, eds.),pp. 1–10, Nova Science Publishers, Huntington, NY, 2001.

101. A. Bottcher, Yu.I. Karlovich, and V.S. Rabinovich: Singular integral operatorswith complex conjugation from the viewpoint of pseudodifferential operators.Operator Theory: Adv. and Appl. 121 (2001), 36–59.

102. A. Bottcher, A.V. Chithra, and M.N.N. Namboodiri: Approximation of ap-proximation numbers by truncation. Integral Equations and Operator Theory39 (2001), 387–395.

103. A. Bottcher, Yu.I. Karlovich, and I. Spitkovsky: Toeplitz operators with semi-almost periodic matrix symbols on Hardy spaces. Acta Applicandae Mathe-maticae 65 (2001), 115–136.

Publications of Albrecht Bottcher xix

104. A. Bottcher: One more proof of the Borodin–Okounkov formula for Toeplitzdeterminants. Integral Equations and Operator Theory 41 (2001), 123–125.

105. A. Bottcher and M. Seybold: Discrete one-dimensional zero-order pseudodif-ferential operators on spaces with Muckenhoupt weight. Algebra i Analiz 13(2001), 116–129 and St. Petersburg Math. J. 13 (2002), 241–252.

106. A. Bottcher, S. Grudsky, and I. Spitkovsky: Toeplitz operators with frequencymodulated semi-almost periodic symbols. J. Fourier Analysis Appl. 7 (2001),523–535.

107. A. Bottcher and S. Grudsky: Condition numbers of large Toeplitz-like matri-ces. Contemp. Math. 280 (2001), 273–299.

108. A. Bottcher and Yu.I. Karlovich: Cauchy’s singular integral operator and itsbeautiful spectrum. Operator Theory: Adv. and Appl. 129 (2001), 109–142.

109. A. Bottcher, M. Embree, and V.I. Sokolov: Infinite Toeplitz and Laurentmatrices with localized impurities. Linear Algebra Appl. 343/344 (2002), 101–118.

110. A. Bottcher, M. Embree, and M. Lindner: Spectral approximation of bandedLaurent matrices with localized random perturbations. Integral Equations andOperator Theory 42 (2002), 142–165.

111. A. Bottcher and S. Grudsky: Can spectral value sets of Toeplitz band matricesjump? Linear Algebra Appl. 351/352 (2002), 99–116.

112. A. Bottcher, S. Grudsky, and A. Kozak: On the distance of a large Toeplitzband matrix to the nearest singular matrix. Operator Theory: Adv. and Appl.135 (2002), 101–106.

113. A. Bottcher:On the determinant formulas by Borodin, Okounkov, Baik, Deift,and Rains. Operator Theory: Adv. and Appl. 135 (2002), 91–99.

114. A. Bottcher: Essay on Bernd Silbermann. Operator Theory: Adv. and Appl.135 (2002), 1–12.

115. A. Bottcher, M. Embree, and L.N. Trefethen: Piecewise continuous Toeplitzmatrices and operators: slow approach to infinity. SIAM J. Matrix AnalysisAppl. 24 (2002), 484–489.

116. A. Bottcher, M. Embree, and V.I. Sokolov: On large Toeplitz band matriceswith an uncertain block. Linear Algebra Appl. 366 (2003), 87–97.

117. D. Bini and A. Bottcher: Polynomial factorization through Toeplitz matrixcomputations. Linear Algebra Appl. 366 (2003), 25–37.

118. A. Bottcher, S. Grudsky, and I. Spitkovsky: On the essential spectrum ofToeplitz operators with semi-almost periodic symbols. Operator Theory: Adv.and Appl. 142 (2003), 59–77.

119. A. Bottcher, M. Embree, and V.I. Sokolov: The spectra of large Toeplitz bandmatrices with a randomly perturbed entry. Mathematics of Computation 72(2003), 1329–1348.

xx Publications of Albrecht Bottcher

120. A. Bottcher, S. Grudsky, and I. Spitkovsky: Block Toeplitz operators withfrequency-modulated semi-almost periodic symbols. Int. J. Math. Math. Sci.2003:34 (2003), 2157–2176.

121. A. Bottcher and S. Grudsky: The norm of the product of a large matrix and arandom vector. Electronic Journal of Probability 8 (2003), Paper no. 7, pages1–29.

122. A. Bottcher and S. Grudsky: Asymptotic spectra of dense Toeplitz matricesare unstable. Numerical Algorithms 33 (2003), 105–112.

123. A. Bottcher and S. Grudsky: Toeplitz matrices with slowly growing pseu-dospectra. In: Factorization, Singular Operators and Related Problems inHonour of Georgii Litvinchuk (S. Samko, A. Lebre, A.F. dos Santos, eds.),pp. 43–54, Kluwer Academic Publishers, Dordrecht, 2003.

124. A. Bottcher, Yu.I. Karlovich, and I. Spitkovsky: The C*-algebra of singularintegral operators with semi-almost periodic coefficients. J. Funct. Analysis204 (2003), 445–484.

125. A. Bottcher and S. Grudsky: Fejer means and norms of large Toeplitz matri-ces. Acta Sci. Math. (Szeged) 69 (2003), 889–900.

126. A. Bottcher and B. Silbermann: Erhard Meister – friend and colleague. Op-erator Theory: Adv. and Appl. 147 (2004), p. 67.

127. A. Bottcher and S. Grudsky: Asymptotically good pseudomodes for Toeplitzmatrices and Wiener–Hopf operators. Operator Theory: Adv. and Appl. 147(2004), 175–188.

128. A. Bottcher: Transient behavior of powers and exponentials of large Toeplitzmatrices. Electronic Transactions on Numerical Analysis (ETNA) 18 (2004),1–41.

129. A. Bottcher, S. Grudsky, and E. Ramırez de Arellano: Algebras of Toeplitzoperators with oscillating symbols. Revista Matematica Iberoamericana 20(2004), 647–671.

130. A. Bottcher: The constants in the asymptotic formulas by Rambour andSeghier for inverses of Toeplitz matrices. Integral Equations and OperatorTheory 50 (2004), 43–55.

131. A. Bottcher, S. Grudsky, and E. Ramırez de Arellano: Approximating in-verses of Toeplitz matrices by circulant matrices. Methods and Applicationsof Analysis 11 (2004), 211–220.

132. A. Bottcher and K. Rost: Topics in the numerical linear algebra of Toeplitzand Hankel matrices. GAMM-Mitteilungen 27 (2004), 174–188.

133. Z. Hurak and A. Bottcher: MIMO �1-optimal control via block Toeplitz op-erators. In: Proceedings of 16th International Symposium on MathematicalTheory of Networks and Systems (MTNS’04), Katholieke Universiteit Leu-ven, 2004.

Publications of Albrecht Bottcher xxi

134. A. Bottcher and D. Wenzel: How big can the commutator of two matrices beand how big is it typically? Linear Algebra Appl. 403 (2005), 216–228.

135. A. Bottcher and S. Grudsky: Structured condition numbers of large Toeplitzmatrices are rarely better than usual condition numbers. Numerical LinearAlgebra with Applications 12 (2005), 95–102.

136. A. Bottcher, I. Gohberg, and B. Silbermann: Georg Heinig (1947–2005) InMemoriam. Integral Equations and Operator Theory 53 (2005), 297–300.

137. A. Bottcher and P. Otte: The first Szego limit theorem for non-selfadjointoperators in the Følner algebra. Mathematica Scandinavica 97 (2005), 115–126.

138. A. Bottcher and H. Widom: Two elementary derivations of the pure Fisher–Hartwig determinant. Integral Equations and Operator Theory 53 (2005),593–596.

139. A. Bottcher, S. Grudsky, and E. Ramırez de Arellano: On the asymptoticbehavior of the eigenvectors of large banded Toeplitz matrices. Math. Nachr.279 (2006), 121–129.

140. A. Bottcher: On the problem of testing the structure of a matrix by displace-ment operations. SIAM J. Numerical Analysis 44 (2006), 41–54.

141. Z. Hurak, A. Bottcher, and M. Sebek: Minimum distance to the range of abanded lower triangular Toeplitz operator in �1 and application in �1-optimalcontrol. SIAM J. Control Optim. 45 (2006), 107–122.

142. A. Bottcher, B. Hofmann, U. Tautenhahn, and M. Yamamoto: Convergencerates for Tikhonov regularization from different kinds of smoothness condi-tions. Applicable Analysis 85 (2006), 555–578.

143. A. Bottcher: Review of “Spectra and Pseudospectra: The Behavior of Non-normal Matrices and Operators” by L.N. Trefethen and M. Embree. LinearAlgebra Appl. 416 (2006), 1098–1101.

144. A. Bottcher and H. Widom: From Toeplitz eigenvalues through Green’s ker-nels to higher-order Wirtinger–Sobolev inequalities. Operator Theory: Adv.and Appl. 171 (2006), 73–87.

145. A. Bottcher and H. Widom: On the eigenvalues of certain canonical higher-order ordinary differential operators. J. Math. Analysis Appl. 322 (2006),990–1000.

146. A. Bottcher: Schatten norms of Toeplitz matrices with Fisher–Hartwig sin-gularities. Electronic Journal of Linear Algebra (ELA) 15 (2006), 251–259.

147. A. Bottcher and H. Widom: Szego via Jacobi. Linear Algebra Appl. 419(2006), 656–667.

148. A. Bottcher and D. Wenzel: On the verification of linear equations and theidentification of the Toeplitz-plus-Hankel structure. Operator Theory: Adv.and Appl. 170 (2007), 43–51.

xxii Publications of Albrecht Bottcher

149. J. Gutierrez-Gutierrez, P.M. Crespo, and A. Bottcher: Functions of bandedHermitian block Toeplitz matrices in signal processing. Linear Algebra Appl.422 (2007), 788–807.

150. A. Bottcher, D. Potts, and D. Wenzel: A probability argument in favor ofignoring small singular values. Operators and Matrices 1 (2007), 31–43.

151. A. Bottcher, J. Gutierrez-Gutierrez, and P.M. Crespo: Mass concentration inquasicommutators of Toeplitz matrices. J. Comput. Appl. Math. 205 (2007),129–148.

152. A. Bottcher and D. Potts: Probability against condition number and samplingof multivariate trigonometric random polynomials. Electronic Transactionson Numerical Analysis (ETNA) 26 (2007), 178–189.

153. A. Bottcher and J. Virtanen: Norms of Toeplitz matrices with Fisher–Hartwigsymbols. SIAM J. Matrix Analysis Appl. 29 (2007), 660–671.

154. A. Bottcher, A. Karlovich, and B. Silbermann: Generalized Krein algebrasand asymptotics of Toeplitz determinants. Methods of Functional Analysisand Topology 13 (2007), 236–261.

155. A. Bottcher and S. Grudsky: Uniform boundedness of Toeplitz matrices withvariable coefficients. Integral Equations and Operator Theory 60 (2008), 313–328.

156. A. Bottcher, S. Grudsky, and M. Schwartz: Some problems concerning thetest functions in the Szego and Avram–Parter theorems. Operator Theory:Adv. and Appl. 187 (2008), 81–93.

157. A. Bottcher, S. Grudsky, and E.A. Maksimenko: The Szego and Avram–Parter theorems for general test functions. C. R. Math. Acad. Sci. Paris 346(2008), 749–752.

158. A. Bottcher, S. Grudsky, and E.A. Maksimenko: Pushing the envelope of thetest functions in the Szego and Avram–Parter theorems. Linear Algebra Appl.429 (2008), 346–366.

159. A. Bottcher: Orthogonal symmetric Toeplitz matrices. Complex Analysis andOperator Theory 2 (2008), 285–298.

160. A. Bottcher and D. Wenzel: Rigorous stochastic bounds for the error in largecovariance matrices. Math. Methods Appl. Sci. 31 (2008), 1209–1220.

161. A. Bottcher: Linear and one-dimensional. In: Israel Gohberg and Friends(H. Bart, T. Hempfling, M.A. Kaashoek, editors), pp. 291–293, BirkhauserVerlag, Basel, 2008.

162. A. Bottcher and D. Wenzel: The Frobenius norm and the commutator. LinearAlgebra Appl. 429 (2008), 1864–1885.

163. A. Bottcher, S. Grudsky, and J. Unterberger: Asymptotic pseudomodes ofToeplitz matrices. Operators and Matrices 2 (2008), 525–541.

164. A. Bottcher and M. Lindner: Pseudospectrum. Scholarpedia 3(3):2680 (2008).

Publications of Albrecht Bottcher xxiii

165. A. Bottcher and P. Dorfler:On the best constants in inequalities of the Markovand Wirtinger types for polynomials on the half-line. Linear Algebra Appl.430 (2009), 1057–1069.

166. A. Bottcher, S. Grudsky, E.A. Maksimenko, and J. Unterberger: The first-order asymptotics of the extreme eigenvectors of certain Hermitian Toeplitzmatrices. Integral Equations and Operator Theory 63 (2009), 165–180.

167. A. Bottcher, S. Kunis, and D. Potts: Probabilistic spherical Marcinkiewicz–Zygmund inequalities. J. Approx. Theory 157 (2009), 113–126.

168. A. Bottcher and I. Spitkovsky: Drazin inversion in the von Neumann algebragenerated by two orthogonal projections. J. Math. Analysis Appl. 358 (2009),403–409.

169. A. Bottcher, S. Grudsky, and E.A. Maksimenko: On the asymptotics of alleigenvalues of Hermitian Toeplitz band matrices (Russian). Dokl. Akad. Nauk428 (2009), 153–156. Engl. transl. in Doklady Math. 80 (2009), 662–664.

170. A. Bottcher and P. Dorfler: Weighted Markov-type inequalities, norms ofVolterra operators, and zeros of Bessel functions. Math. Nachr. 283 (2010),40–57.

171. A. Bottcher and I. Spitkovsky: A gentle guide to the basics of two projectionstheory. Linear Algebra Appl. 432 (2010), 1412–1459.

172. A. Bottcher, S. Grudsky, and E.A. Maksimenko: Inside the eigenvalues of cer-tain Hermitian Toeplitz band matrices. J. Comput. Appl. Math. 233 (2010),2245–2264.

173. A. Bottcher and S. Grudsky: Variable-coefficient Toeplitz matrices with sym-bols beyond the Wiener algebra. Operator Theory: Adv. and Appl. 199 (2010),192–202.

174. A. Bottcher, S. Grudsky, and E.A. Maksimenko: On the structure of theeigenvectors of large Hermitian Toeplitz band matrices. Operator Theory:Adv. and Appl. 210 (2010), 15–36.

175. A. Bottcher and P. Dorfler: On the best constants in Markov-type inequalitiesinvolving Laguerre norms with different weights. Monatshefte f. Math. 161(2010), 357–367.

176. A. Bottcher, H. Brunner, A. Iserles, and S.P. Nørsett: On the singular valuesand eigenvalues of the Fox-Li and related operators. New York J. Math. 16(2010), 539–561.

177. M. Bogoya, A. Bottcher, S. Grudsky, and E.A. Maksimenko: Eigenvalues ofHessenberg Toeplitz matrices generated by symbols with several singularities.Commun. Math. Analysis, Conf. 03 (2011), 23–41.

178. A. Bottcher and P. Dorfler: On the best constants in Markov-type inequalitiesinvolving Gegenbauer norms with different weights. Operators and Matrices5 (2011), 261–272.

xxiv Publications of Albrecht Bottcher

179. A. Bottcher, S. Grudsky, and R.M. Porter: European double-barrier optionswith a compound Poisson component. In: Progress in Economics Research,Vol. 18 (A. Tavidze, ed.), pp. 315–331, Nova Science Publishers, Huntington,NY, 2011.

180. A. Bottcher and P. Dorfler: Inequalities of the Markov type for partial deriva-tives of polynomials in several variables. J. Integral Equations Appl. 23 (2011),1–37.

181. A. Bottcher: The algebraic Riccati equation with Toeplitz matrices as coeffi-cients. Electronic Journal of Linear Algebra (ELA) 22 (2011), 348–362.

182. A. Bottcher, S. Grudsky, and A. Iserles: Spectral theory of large Wiener–Hopfoperators with complex-symmetric kernels and rational symbols. Math. Proc.Cambridge Phil. Soc. 151 (2011), 161–191.

183. A. Bottcher and I. Spitkovsky: On certain finite-dimensional algebras gener-ated by two idempotents. Linear Algebra Appl. 435 (2011), 1823–1836.

184. A. Bottcher, S. Grudsky, D. Huybrechs, and A. Iserles: First-order trace for-mulae for the iterates of the Fox–Li operator. Operator Theory: Adv. andAppl. 218 (2012), 207–224.

185. M. Bogoya, A. Bottcher, and S. Grudsky: Asymptotics of individual eigenval-ues of a class of large Hessenberg Toeplitz matrices. Operator Theory: Adv.and Appl. 220 (2012), 77–95.

186. M. Bogoya, A. Bottcher, S. Grudsky, and E.A. Maksimenko: Eigenvectors ofHessenberg Toeplitz matrices and a problem by Dai, Geary, and Kadanoff.Linear Algebra Appl. 436 (2012), 3480–3492.

187. M. Bogoya, A. Bottcher, and S. Grudsky: Eigenvalues of Hermitian Toeplitzmatrices with polynomially increasing entries. Journal of Spectral Theory 2(2012), 267–292.

188. A. Bottcher and I. Spitkovsky: Group inversion in certain finite-dimensionalalgebras generated by two idempotents. Indagationes Mathematicae 23 (2012),715–732.

189. A. Bottcher, S. Grudsky, and A. Iserles: The Fox–Li operator as a test anda spur for Wiener–Hopf theory. In: Essays in Mathematics and Its Applica-tions, in Honor of Stephen Smale’s 80th Birthday, pp. 37–48, Springer-Verlag,Heidelberg, 2012.

190. A. Bottcher and A. Pietsch: Orthogonal and skew-symmetric operators in realHilbert space. Integral Equations and Operator Theory 74 (2012), 497–511.

191. A. Bottcher and A. Perala: The index formula of Douglas for block Toeplitzoperators on the Bergman space of the ball. Operator Theory: Adv. and Appl.228 (2013), 39–55.

192. A. Bottcher and I. Spitkovsky: The factorization problem: some known resultsand open questions. Operator Theory: Adv. and Appl. 229 (2013), 101–122.

Publications of Albrecht Bottcher xxv

193. A. Bottcher and M. Halwass: Wiener–Hopf and spectral factorization of realpolynomials by Newton’s method. Linear Algebra Appl. 438 (2013), 4760–4805.

194. A. Bottcher and I. Spitkovsky: Classification of the finite-dimensional alge-bras generated by two tightly coupled idempotents. Linear Algebra Appl. 439(2013), 538–551.

195. A. Bottcher: An operator theoretic approach to the brickwork Ising model withsecond-neighbor interactions. Linear Algebra Appl. 439 (2013), 675–685.

196. A. Bottcher: Best constants for Markov type inequalities in Hilbert spacenorms. In: Recent Trends in Analysis, Proceedings of the Conference in Honorof Nikolai Nikolski, Bordeaux 2011, pp. 73–83, Theta, Bucharest, 2013.

197. A. Bottcher and I. Spitkovsky: Special types of matrices. Chapter 22 of theHandbook of Linear Algebra, 2nd edition, edited by Leslie Hogben, Chapman& Hall/CRC, Boca Raton, FL, 2013.

198. A. Bottcher and M. Halwass: A Newton method for canonical Wiener–Hopfand spectral factorization of matrix polynomials. Electronic Journal of LinearAlgebra (ELA) 26 (2013), 873–897.

199. A. Bottcher: Borodin–Okounkov and Szego for Toeplitz operators on modelspaces. Integral Equations and Operator Theory 78 (2014), 407–414.

200. A. Bottcher: On Hurwitz stable polynomials with integer coefficients. Com-putational Methods and Function Theory 14 (2014), 139–156.

201. A. Bottcher and M. Halwass: Canonical Wiener–Hopf and spectral factoriza-tion of large-degree matrix polynomials. Proceedings in Applied Mathematicsand Mechanics (PAMM) 14 (2014), 817–818.

202. M. Bogoya, A. Bottcher, S. Grudsky, and E.A. Maximenko: Eigenvalues ofHermitian Toeplitz matrices with smooth simple-loop symbols. J. Math. Anal-ysis Appl. 422 (2015), 1308–1334.

203. A. Bottcher, L. Fukshansky, S.R. Garcia, and H. Maharaj: Toeplitz deter-minants with perturbations in the corners. J. Funct. Analysis 268 (2015),171–193.

204. A. Bottcher, L. Fukshansky, S.R. Garcia, and H. Maharaj: On lattices gen-erated by finite Abelian groups. SIAM J. Discrete Math. 29 (2015), 382–404.

205. M. Bogoya, A. Bottcher, S. Grudsky, and E.A. Maximenko: Maximum normversions of the Szego and Avram–Parter theorems for Toeplitz matrices. J.Approx. Theory 196 (2015), 79–100.

206. A. Bottcher, D. Kowerko, and R.K.O. Sigel: Explicit analytic equations formultimolecular thermal melting curves. Biophysical Chemistry 202 (2015),32–39.

207. A. Bottcher, L. Fukshansky, S.R. Garcia, and H. Maharaj: Lattices fromHermitian function fields. J. Algebra 447 (2016), 560–579.

xxvi Publications of Albrecht Bottcher

208. M. Bogoya, A. Bottcher, S. Grudsky, and E.A. Maximenko: Eigenvectors ofHermitian Toeplitz matrices with smooth simple-loop symbols. Linear AlgebraAppl. 493 (2016), 606–637.

209. A. Bottcher and F. Kittaneh: The limit of the zero set of polynomials of theFibonacci type. J. Number Theory 163 (2016), 89–100.

210. A. Bottcher: The part of my path I walked together with Sergei Grudsky. Bol.Soc. Mat. Mex. 22 (2016), 309–327.

211. M. Bogoya, A. Bottcher, and E.A. Maximenko: From convergence in distri-bution to uniform convergence. Bol. Soc. Mat. Mex. 22 (2016), 695–710.

212. A. Bottcher, H. Langenau, and H. Widom: Schatten class integral operatorsoccurring in Markov-type inequalities. Operator Theory: Adv. and Appl. 255(2016), 91–104.

213. A. Bottcher, L. Fukshansky, S.R. Garcia, H. Maharaj, and D. Needell: Latticesfrom equiangular tight frames. Linear Algebra Appl. 510 (2016), 395–420.

214. A. Bottcher and F.-O. Speck: On the symmetrization of general Wiener–Hopfoperators. J. Operator Theory 76 (2016), 335–349.

215. A. Bottcher, L. Fukshansky, S.R. Garcia, and H. Maharaj: Lattices fromAbelian groups. Oberwolfach Reports 13 (2016) 121–124.

216. A. Bottcher: The Duduchava–Roch formula. Operator Theory: Adv. andAppl. 258 (2017), 1–19.

217. A. Bottcher and C. Rebs: On the constants in Markov inequalities for theLaplace operator on polynomials with the Laguerre norm. Asymptotic Anal-ysis, to appear.

218. A. Bottcher, L. Fukshansky, S.R. Garcia, and H. Maharaj: Lattice theory andToeplitz determinants. Operator Theory: Adv. and Appl., to appear.

219. A. Bottcher: Index formulas for Toeplitz operators, approximate identities,and the Wolf-Havin theorem. To appear.

220. A. Bottcher, C. Garoni, and S. Serra-Capizzano: Exploration of Toeplitz-likematrices with unbounded symbols: not a purely academic journey. To appear.

221. A. Bottcher, J.M. Bogoya, S.M. Grudsky, and E.A. Maximenko: Asymptoticformulas for the eigenvalues and eigenvectors of Toeplitz matrices. To appear(in Russian).

222. A. Bottcher, S. Eisenbarth, L. Fukshansky, S.R. Garcia, and H. Maharaj:Spherical 2-designs and lattices from Abelian groups. To appear.