
Journal of Lie Theory 21 (2011), No. 2, 427456 Copyright Heldermann Verlag 2011 Nonabelian Harmonic Analysis and Functional Equations on Compact Groups Jinpeng An LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, P.R.China anjinpeng@gmail.com Dilian Yang Dept. of Mathematics and Statistics, University of Windsor, Windsor, ON N9B 3P4, Canada dyang@uwindsor.ca Making use of nonabelian harmonic analysis and representation theory, we solve the functional equation f_{1}(xy) + f_{2}(yx) + f_{3}(xy^{1}) + f_{4}(y^{1}x) = f_{5}(x)f_{6}(y) on arbitrary compact groups, where all f_{i}'s are unknown square integrable functions. It turns out that the structure of its general solution is analogous to that of linear differential equations. Consequently, various special cases of the above equation, in particular, the Wilson equation and the d'Alembert long equation, are solved on compact groups. Keywords: Functional equation, Fourier transform, representation theory. MSC: 39B52, 22C05, 43A30, 22E45 [ Fulltextpdf (250 KB)] for subscribers only. 