Generalized derivations and generalized exponential monomials on hypergroups

TL;DR

This paper explores the relationship between generalized exponential polynomials and higher order derivations in the measure algebra of commutative hypergroups, extending previous work on exponential monomials.

Contribution

It establishes a connection between generalized exponential polynomials and higher order derivations on measure algebras of commutative hypergroups, advancing the theoretical understanding.

Findings

Identified the link between exponential polynomials and derivations

Extended previous results on exponential monomials

Provided new insights into hypergroup measure algebras

Abstract

In one of our former papers {\it Endomorphisms of the measure algebra of commutative hypergroups arXiv:2204.07499 we considered exponential monomials on hypergroups and higher order derivations of the corresponding measure algebra. Continuing with this, we are now looking for the connection between the generalized exponential polynomials of a commutative hypergroup and the higher order derivations of the corresponding measure algebra.