An integral functional equation on groups under two measures

Abstract Let G be a locally compact Hausdorff group, let σ be a continuous involutive automorphism on G, and let μ, ν be regular, compactly supported, complex-valued Borel measures on G. We find the continuous solutions 𝑓 : G → C of the functional equ...

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Autores principales:	Fadli,B., Zeglami,D., Kabbaj,S.
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2018
Materias:	Functional equation Van Vleck Kannappan involutive automorphism group character.
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000300565
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spelling	oai:scielo:S0716-091720180003005652018-10-10An integral functional equation on groups under two measuresFadli,B.Zeglami,D.Kabbaj,S. Functional equation Van Vleck Kannappan involutive automorphism group character. Abstract Let G be a locally compact Hausdorff group, let σ be a continuous involutive automorphism on G, and let μ, ν be regular, compactly supported, complex-valued Borel measures on G. We find the continuous solutions 𝑓 : G → C of the functional equation in terms of continuous characters of G. This equation provides a common generalization of many functional equations (d’Alembert’s, Cauchy’s, Gajda’s, Kannappan’s, Stetkær’s, Van Vleck’s equations...). So, a large class of functional equations will be solved.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.37 n.3 20182018-09-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000300565en10.4067/S0716-09172018000300565
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Functional equation Van Vleck Kannappan involutive automorphism group character.
spellingShingle	Functional equation Van Vleck Kannappan involutive automorphism group character. Fadli,B. Zeglami,D. Kabbaj,S. An integral functional equation on groups under two measures
description	Abstract Let G be a locally compact Hausdorff group, let σ be a continuous involutive automorphism on G, and let μ, ν be regular, compactly supported, complex-valued Borel measures on G. We find the continuous solutions 𝑓 : G → C of the functional equation in terms of continuous characters of G. This equation provides a common generalization of many functional equations (d’Alembert’s, Cauchy’s, Gajda’s, Kannappan’s, Stetkær’s, Van Vleck’s equations...). So, a large class of functional equations will be solved.
author	Fadli,B. Zeglami,D. Kabbaj,S.
author_facet	Fadli,B. Zeglami,D. Kabbaj,S.
author_sort	Fadli,B.
title	An integral functional equation on groups under two measures
title_short	An integral functional equation on groups under two measures
title_full	An integral functional equation on groups under two measures
title_fullStr	An integral functional equation on groups under two measures
title_full_unstemmed	An integral functional equation on groups under two measures
title_sort	integral functional equation on groups under two measures
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2018
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000300565
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An integral functional equation on groups under two measures

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