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

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

All paper is related with the non-zero continuous solutions f : G → ℂ of the functional equation f(xσ(y))+f(τ(y)x)=2f(x)f(y),     x,y∈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...

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Bibliographic Details
Main Authors: EL-Fassi Iz-iddine, Chahbi Abdellatif, Kabbaj Samir
Format: Article
Language:English
Published: Sciendo 2017-08-01
Series:Acta Universitatis Sapientiae: Mathematica
Subjects:
functional equation
non-abelian fourier transform
representation of a compact group
39b52
22c05
43a30
22e45
Online Access:https://doi.org/10.1515/ausm-2017-0004
Description
Summary:All paper is related with the non-zero continuous solutions f : G → ℂ of the functional equation f(xσ(y))+f(τ(y)x)=2f(x)f(y),     x,y∈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:
ISSN:2066-7752

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