An elementary approach to asymptotic behavior in the Ces\`aro sense and applications to the Laplace and Stieltjes transforms

TL;DR

This paper introduces a simple method for analyzing the asymptotic behavior of generalized functions in the Cesàro sense, utilizing Yosida's subspace of Mikusiński operators, with applications to Laplace and Stieltjes transforms.

Contribution

It presents an elementary approach based on Mikusiński operators for studying asymptotic behavior, offering new insights into Laplace and Stieltjes transform applications.

Findings

New elementary method for Cesàro asymptotics

Applications to Laplace and Stieltjes transforms demonstrated

Enhanced understanding of generalized functions' asymptotic behavior

Abstract

We present a elementary approach to asymptotic behavior of generalized functions in the Ces\`aro sense. Our approach is based on Yosida's subspace of Mikusi\'nski operators. Applications to Laplace and Stieltjes transforms are given.