Nonabelian harmonic analysis and functional equations on compact groups

2008/09/04 by Jinpeng An, An, Jinpeng, Dilian Yang +1
Computer Science · Mathematics · #22C05 #22E45 #39B52 #43A30 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Mathematical Analysis and Transform Methods #math.FA #msc:22C05 #msc:22E45 #msc:39B52 #msc:43A30

paper · pdf · doi:10.48550/arxiv.0809.0911

29 pages

arxiv created 2008/09/04 · openalex publication_date 2008/09/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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