TL;DR
This paper presents a unified and accessible approach to solving key functional equations on compact groups by exploring their connections with harmonic analysis and representation theory.
Contribution
It introduces a novel unified method for solving the d'Alembert, Wilson, and d'Alembert long equations on compact groups.
Findings
Unified solution framework for three functional equations
Connections established between functional equations and harmonic analysis
Accessible approach simplifies solving complex equations
Abstract
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.
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