Moment functions and exponential monomials on commutative hypergroups

TL;DR

This paper proves that on a commutative hypergroup, exponential monomials with a one-dimensional sine function subspace are linear combinations of generalized moment functions, linking specific function properties to algebraic structure.

Contribution

It establishes a new characterization of exponential monomials in commutative hypergroups based on the dimensionality of sine function subspaces.

Findings

Exponential monomials with one-dimensional sine subspaces are linear combinations of generalized moment functions.

Provides a structural link between sine functions and moment functions on hypergroups.

Enhances understanding of function spaces on commutative hypergroups.

Abstract

The purpose of this paper is to prove that if on a commutative hypergroup an exponential monomial has the property that the linear subspace of all sine functions in its variety is one dimensional, then this exponential monomial is a linear combination of generalized moment functions.