Illinois Journal of Mathematics

Generalization of the Wiener–Ikehara theorem

Gregory Debruyne and Jasson Vindas

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We study the Wiener–Ikehara theorem under the so-called log-linearly slowly decreasing condition. Moreover, we clarify the connection between two different hypotheses on the Laplace transform occurring in exact forms of the Wiener–Ikehara theorem, that is, in “if and only if” versions of this theorem.

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Illinois J. Math., Volume 60, Number 2 (2016), 613-624.

Received: 29 November 2016
Revised: 30 January 2017
First available in Project Euclid: 11 July 2017

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Zentralblatt MATH identifier

Primary: 11M45: Tauberian theorems [See also 40E05] 40E05: Tauberian theorems, general


Debruyne, Gregory; Vindas, Jasson. Generalization of the Wiener–Ikehara theorem. Illinois J. Math. 60 (2016), no. 2, 613--624. doi:10.1215/ijm/1499760025.

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