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A general quantified Ingham-Karamata Tauberian theorem (2411.03809v1)
Published 6 Nov 2024 in math.CA, math.CV, and math.NT
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.
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