A quantified Tauberian theorem for the Laplace-Stieltjes transform

2017/11/21 by Markus Hartlapp
Computer Science · Engineering · Mathematics · #Abelian and tauberian theorems #Advanced Mathematical Modeling in Engineering #Bounded function #Bounded variation #Calculus (dental) #Dirichlet distribution #Fourier transform #Integral equation #Laplace transform #Laplace–Stieltjes transform #Mathematical analysis #Mathematics #Nonlinear Differential Equations Analysis #Pure mathematics #Riemann–Stieltjes integral #Stability and Controllability of Differential Equations #math.FA

paper · pdf · doi:10.1007/s00013-018-1164-2

13 pages, no figures

arxiv created 2017/11/21 · openalex publication_date 2018/02/13 · arxiv updated 2018/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We prove a quantified Tauberian theorem involving Laplace-Stieltjes transform which is motivated by the work of Ingham and Karamata. For this, we consider functions which are locally of bounded variation and, therefore, get a generalisation of some results of Batty and Duyckaerts. We show that our theorem can be applied to special Dirichlet series.

Citations

• Newman's Short Proof of the Prime Number Theorem
• Simple Analytic Proof of the Prime Number Theorem
• Simple Analytic Proof of the Prime Number Theorem
• Newman's Short Proof of the Prime Number Theorem