A note on Tauberian Theorems of Exponential Type

TL;DR

This paper unifies several classical Tauberian theorems of exponential type into a single theorem by analyzing their structure and relationships, simplifying understanding and application of these results.

Contribution

It identifies the structure of classical Tauberian theorems of exponential type and consolidates them into one theorem using recent relationship findings.

Findings

Unified classical Tauberian theorems into a single theorem.

Clarified relationships among components of these theorems.

Simplified the theoretical framework for exponential type Tauberian theorems.

Abstract

Tauberian Theorems of exponential type provided by Kohlbecker, de Bruijn, and Kasahara are proved in only one Tauberian theorem. To this aim, the structure of those classical tauberian theorems is identified and, using a relationship recently proved by Cadena and Kratz, the relationships among its components are given.