Theoretical analysis demonstrates generalized versions of the Wiener–Ikehara theorem using Laplace transform real parts, highlighting a streamlined Tauberian proof of Blackwell's renewal theorem.
We establish new versions of the Wiener–Ikehara theorem where only boundary assumptions on the real part of the Laplace transform are imposed. Our results generalize and improve a recent theorem of Koga (2021). As an application, we give a quick Tauberian proof of Blackwell's renewal theorem.
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Chen et al. (2026) studied this question.
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