Nonabelian harmonic analysis and functional equations on compact groups
Abstract
Making use of nonabelian harmonic analysis and representation theory, we solve the functional equation f1(xy)+f2(yx)+f3(xy-1)+f4(y-1x)=f5(x)f6(y) on arbitrary compact groups. The structure of its general solution is completely described. Consequently, several special cases of the above equation, in particular, the Wilson equation and the d'Alembert long equation, are solved on compact groups.
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