Moment functions on groups

TL;DR

This paper characterizes generalized moment functions on groups, showing they are exponential polynomials described by Bell polynomials, with implications for higher-rank cases.

Contribution

It provides new characterization theorems for generalized moment functions on groups, linking them to exponential polynomials and Bell polynomials.

Findings

Moment functions are exponential polynomials.

Characterizations extend to higher-rank cases.

Results connect moment functions with Bell polynomials.

Abstract

The main purpose of this work is to prove characterization theorems for generalized moment functions on groups. According one of the main results these are exponential polynomials that can be described with the aid of complete (exponential) Bell polynomials. These characterizations will be immediate consequences of our main result about the characterization of generalized moment functions of higher rank.