In Memory of Ray KunzeKenneth I. Gross and Edward N. Wilson
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oto
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Ken
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Ray Kunze
Ray Alden Kunzepassed away on May 21,2014, after a lengthyillness. Ray was a long-time member of theAMS, served on the AMSCouncil and a numberof American Mathemat-ical Society committees,and was selected asan Inaugural Fellow in2012. He published overfifty research articles,among which were sem-inal results of primary
importance in representation theory and harmonicanalysis. As well, his classic textbook on linearalgebra, co-authored with Kenneth Hoffman, wastranslated into many languages and used aroundthe world.
Ray was born March 7, 1928, in Des Moines,Iowa, but lived much of his youth in the areaaround Milwaukee, Wisconsin. He received hisbachelor of science and master of science degreesin mathematics from the University of Chicago.A talented tennis player, he was captain of theUniversity of Chicago tennis team. He playedcompetitive tennis and then table tennis all of hislife. His graduate studies were interrupted duringthe early 1950s by military service, during whichperiod he served as a mathematical analyst in theDepartment of Defense. Upon completion of histour of duty he returned to his doctoral studies atthe University of Chicago and in 1957 received hisdoctor of philosophy degree in mathematics.
Ray began his mathematics career on the facultyof MIT and over the ensuing years served on
Kenneth I. Gross is professor of mathematics at the Univer-sity of Vermont. His email address is [email protected].
Edward N. Wilson is professor of mathematics at Washing-ton University. His email address is [email protected].
For permission to reprint this article, please contact:[email protected].
DOI: http://dx.doi.org/10.1090/noti1283
the faculties of Brandeis University, WashingtonUniversity, the University of California at Irvine,and the University of Georgia. At both Irvine andGeorgia he chaired the Department of Mathematics.He also held numerous visiting positions in theUnited States, including the Institute for AdvancedStudy at Princeton, and in England, Belgium, France,Italy, Germany, Australia, and Taiwan.
Three aspects of Ray’s research can be singledout as especially notable: (i) His joint work withEli Stein in the late 1950s and 1960s (“the Kunze-Stein phenomena”) in which they constructeduniformly bounded nonunitary representationsof a semisimple Lie group G and showed thatconvolution by an Lp function is a boundedoperator on L2(G) for all 1 ≤ p < 2. There is noanalogue in the classical theory, as convolutionby an Lp function on Rn is bounded only whenp = 1. (ii) His papers on noncommutative Lpspaces associated with a von Neumann algebra,a topic initiated by Irving Segal and JacquesDixmier in the 1950s and which is now a well-established area with hundreds of contributors.(iii) His joint work in the 1970s and 1980s with KenGross on operator-valued Bessel functions (“Gross-Kunze Bessel functions”) and their applicationto noncommutative harmonic analysis and tothe infinite-dimensional representation theory ofsemisimple Lie groups.
Ray was also an inspirational teacher whoadvised eleven doctoral students, a number ofwhom have gone on to distinguished careers andthree of whom are Fellows of the AMS. Thosewho had the great privilege of being his studentreceived the best possible mathematical training.
1190 Notices of the AMS Volume 62, Number 10
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