Belaid Bouikhalene, Samir Kabbaj

Gelfand Pairs and Generalized d'Alembert's and Cauchy's Functional Equations

Abstract:
We show that Cauchy's, d'Alembert's functional equations and their generalizations are the functional equations for bounded spherical functions associated to some Gel'fand pairs. Our results are very close to the ones obtained by Stetk\ae r in (Aequationes Math. 48(1994), No. 2-3, 220-227).

Keywords:
Functional equations, Gel'fand pairs, spherical functions.

MSC 2000: 39B32, 39B42, 22D10, 22D12, 22D15