A general quantified Ingham-Karamata Tauberian theorem
Classical Analysis and ODEs
2024-11-07 v1 Complex Variables
Number Theory
Abstract
We provide a general quantified Ingham-Karamata Tauberian theorem with a flexible one-sided Tauberian condition under several types of boundary behavior for the Laplace transform. Our results in particular improve a theorem by Stahn, removing a vexing restriction on the growth of the Laplace transform. Improving existing optimality results, we also show that the obtained quantified rate is optimal in almost all cases.
Cite
@article{arxiv.2411.03809,
title = {A general quantified Ingham-Karamata Tauberian theorem},
author = {Gregory Debruyne},
journal= {arXiv preprint arXiv:2411.03809},
year = {2024}
}
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58 pages