<abstract xmlns="http://www.w3.org/1999/xhtml">All paper is related with the non-zero continuous solutions f : G → ℂ of the functional equation
<disp-formula><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2017-0004_eq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mtext>f</mtext><mo stretchy="false">(</mo><mtext>x</mtext><mo>σ</mo><mo stretchy="false">(</mo><mtext>y</mtext><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>+</mo><mtext>f</mtext><mo stretchy="false">(</mo><mo>τ</mo><mo stretchy="false">(</mo><mtext>y</mtext><mo stretchy="false">)</mo><mtext>x</mtext><mo stretchy="false">)</mo><mo>=</mo><mn>2</mn><mtext>f</mtext><mo stretchy="false">(</mo><mtext>x</mtext><mo stretchy="false">)</mo><mtext>f</mtext><mo stretchy="false">(</mo><mtext>y</mtext><mo stretchy="false">)</mo><mo>,</mo><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext>x</mtext><mo>,</mo><mtext>y</mtext><mo>∈</mo><mtext>G</mtext><mo>,</mo></math><tex-math>$${\rm{f}}({\rm{x}}\sigma ({\rm{y}})) + {\rm{f}}(\tau ({\rm{y}}){\rm{x}}) = 2{\rm{f}}({\rm{x}}){\rm{f}}({\rm{y}}),\;\;\;\;\;{\rm{x}},{\rm{y}} \in {\rm{G}},$$</tex-math></alternatives></disp-formula>
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:</abstract>

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:

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

Department of Mathematics, Faculty of Sciences

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

All paper is related with the non-zero continuous solutions f : G → ℂ of the functional...

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

Published Online: Aug 05, 2017

Page range: 45 - 52

Received: Dec 07, 2016

DOI: https://doi.org/10.1515/ausm-2017-0004

Keywords
functional equation, non-abelian Fourier transform, representation of a compact group

© 2017 Iz-iddine EL-Fassi et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Aug 05, 2017

Page range: 45 - 52

Received: Dec 07, 2016

DOI: https://doi.org/10.1515/ausm-2017-0004

Keywordsfunctional equation, non-abelian Fourier transform, representation of a compact group

© 2017 Iz-iddine EL-Fassi et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
functional equation, non-abelian Fourier transform, representation of a compact group