Riesz Means and Beurling Moving Averages

TL;DR

This paper explores the relationship between Riesz means and Beurling moving averages, providing Abelian and Tauberian results that connect different summability methods with comparable growth, motivated by applications in probability theory.

Contribution

It offers new theoretical insights into the interplay between Riesz means and Beurling moving averages, including Abelian and Tauberian theorems relating their growth conditions.

Findings

Established connections between Riesz means and Beurling moving averages

Derived Abelian and Tauberian theorems for comparable growth functions

Motivated by applications to strong limit theorems in probability

Abstract

We survey the interplay between the Riesz means and Beurling moving averages of the title, obtaining Abelian and Tauberian results relating different Riesz means (or Beurling moving averages) whose defining functions have comparable growth. The motivation includes strong limit theorems in probability theory.