Endomorphisms and derivations of the measure algebra of commutative hypergroups

TL;DR

This paper investigates the structure of endomorphisms and derivations in the measure algebra of commutative hypergroups, revealing their connection to moment functions and higher order derivations.

Contribution

It characterizes higher order derivations that are also endomorphisms within the measure algebra viewed as a module over continuous functions.

Findings

Identifies the relationship between higher order derivations and moment function sequences.

Provides a complete description of when higher order derivations are endomorphisms.

Establishes the connection between algebraic structures and moment functions in hypergroups.

Abstract

Endomorphisms of the measure algebra of commutative hypergroups are investigated. We focus on derivations and higher order derivations which are closely related to moment function sequences of higher rank. We describe the exact connection between those higher order derivations which are endomorphisms of the measure algebra if it is considered as a module over the ring of continuous functions.