Exponential polynomials on commutative hypergroups

Abstract

Polynomials and exponential polynomials play a fundamental role in the theory of spectral analysis and spectral synthesis on commutative groups. Recently several new results have been published in this field. Spectral analysis and spectral synthesis has been studied on some types of commutative hypergroups, as well. However, a satisfactory definition of exponential monomials on general commutative hypergroups has not been available so far. In his former papers the authors used a special concept on polynomial and Sturm–Liouville-hypergroups. Here we give a general definition which covers the known special cases.