Nonabelian harmonic analysis and functional equations on compact groups

Details Nonabelian harmonic analysis and functional equations on compact groups Nonabelian harmonic analysis and functional equations on compact groups

2008-09-04

arxiv.org/abs/0809.0911v1

Mathematics

Functional Analysis

29 pages

Scientific paper

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. 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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