On The Absence Of Remainders In The Wiener-Ikehara And Ingham-Karamata Theorems: A Constructive Approach
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY(2021)
摘要
We construct explicit counterexamples that show that it is impossible to get any remainder, other than the classical ones, in the Wiener-Ikehara theorem and the Ingham-Karamata theorem under just an additional analytic continuation hypothesis to a half-plane (or even to the whole complex plane).
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关键词
Complex Tauberians, Tauberian theorems with remainder, Wiener-Ikehara theorem, Ingham-Karamata theorem, Laplace transform
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