[1][2] His mathematical research concerned the representation theory of groups and noncommutative harmonic analysis.
[2] Kunze was born in Des Moines, Iowa and grew up near Milwaukee, Wisconsin.
[2] After working as a military mathematical analyst,[1][2] he returned to the University of Chicago, and earned his Ph.D. in 1957 with a dissertation on Fourier transformations supervised by Irving Segal.
[1][2] He has over 50 academic descendants, many of them through his students Paul Sally at Brandeis and Edward N. Wilson at Washington University.
[3] With his advisor Irving Segal, Kunze was the author of the textbook Integrals and Operators (McGraw-Hill, 1968; 2nd ed., Grundlehren der Mathematischen Wissenschaften 228, Springer, 1978).