Solution of a functional equation on compact groups using Fourier analysis

Abdellatif Chahbi, Brahim Fadli, Samir Kabbaj

Abstract


Let \(G\) be a compact group, let \(n \in N\setminus \{0,1\}\) be a fixed element and let \(\sigma\) be a continuous automorphism on \(G\) such that \(\sigma^n=I\). Using the non-abelian Fourier transform, we determine the non-zero continuous solutions \(f:G \to C\) of the functional equation \[ f(xy)+\sum_{k=1}^{n-1}f(\sigma^k(y)x)=nf(x)f(y),\ x,y \in G,\] in terms of unitary characters of \(G\).

Keywords


Functional equation; non-abelian Fourier transform; representation of a compact group.

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References


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DOI: http://dx.doi.org/10.17951/a.2015.69.2.9-15
Date of publication: 2015-12-30 22:51:59
Date of submission: 2015-12-29 21:48:16


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