On Cauchy’s and quadratic type functional equation on locally compact abelian groups

Hajira Dimou


We find the solutions f ;g : G!C of the functional equation å
k2K å l2K Z G f (x+k y+l s)dm(s) = g(x)+k f (y); x;y 2 G;
where (G;+) is a locally compact abelian Hausdorff group, K is a finite automorphism group of G, k = cardK and m is a regular compactly supported complex-valued Borel measure on G such that m(G) = 1 k : This equation provides a common generalization of Cauchy, Jensen and quadratic equations.


automorphism group, K -quadratic functional equation, Cauchy equation.

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