English

Nonabelian harmonic analysis and functional equations on compact groups

Functional Analysis 2008-09-08 v1

Abstract

Making use of nonabelian harmonic analysis and representation theory, we solve the functional equation f1(xy)+f2(yx)+f3(xy1)+f4(y1x)=f5(x)f6(y)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.

Keywords

Cite

@article{arxiv.0809.0911,
  title  = {Nonabelian harmonic analysis and functional equations on compact groups},
  author = {Jinpeng An and Dilian Yang},
  journal= {arXiv preprint arXiv:0809.0911},
  year   = {2008}
}

Comments

29 pages

R2 v1 2026-06-21T11:17:05.899Z