By exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations - the d'Alembert equation, the Wilson equation, and the d'Alembert long equation - on compact groups.

Keywords:

functional equations, Fourier analysis, representation of compact groups functional equations, Fourier analysis, representation of compact groups

MSC Classifications:

39B52, 22C05, 43A30 show english descriptions Equations for functions with more general domains and/or ranges
Compact groups
Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. 39B52 - Equations for functions with more general domains and/or ranges
22C05 - Compact groups
43A30 - Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.

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