Author:
Roukbi Ahmed,Lehlou Fouad,Moussa Mohammed
Abstract
Abstract
Let
{(X,*)}
be a hypergroup and let
{w_{0}}
be a fixed measure on X. In this paper we study the two functional equations
\langle\delta_{x}*\delta_{y}*\omega_{0},g\rangle+\langle\delta_{x}*\delta_{%
\check{y}}*\omega_{0},g\rangle=2g(x)g(y),\quad x,y\in X,
and
\langle\delta_{x}*\delta_{\check{y}}*\omega_{0},f\rangle-\langle\delta_{x}*%
\delta_{y}*\omega_{0},f\rangle=2f(x)f(y),\quad x,y\in X,
where
{g,f:X\to\mathbb{C}}
are continuous and bounded functions to be determined. We express the solutions of the two functional equations in terms of multiplicative maps on
{(X,*)}
. As an application we give the solution of the two functional equations on polynomial and Sturm–Liouville hypergroups.