An extension of a variant of d’Alemberts functional equation on compact groups

Iz-iddine EL-Fassi; Abdellatif Chahbi; Samir Kabbaj

doi:10.1515/ausm-2017-0004

Abstract

All paper is related with the non-zero continuous solutions f : G → ℂ of the functional equation $f (x σ (y)) + f (τ (y) x) = 2 f (x) f (y), x, y \in G,$ $${\rm{f}}({\rm{x}}\sigma ({\rm{y}})) + {\rm{f}}(\tau ({\rm{y}}){\rm{x}}) = 2{\rm{f}}({\rm{x}}){\rm{f}}({\rm{y}}),\;\;\;\;\;{\rm{x}},{\rm{y}} \in {\rm{G}},$$ where σ; τ are continuous automorphism or continuous anti-automorphism defined on a compact group G and possibly non-abelian, such that σ² = τ² = id: The solutions are given in terms of unitary characters of G:

References

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An extension of a variant of d’Alemberts functional equation on compact groups

Abstract

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