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A Tauberian Theorem for Laplace Transforms with Pseudofunction Boundary Behavior

Jaap Korevaar
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Abstract

The prime number theorem provided the chief impulse for complex Tauberian theory, in which the boundary behavior of a transform in the complex plane plays a crucial role. We consider Laplace transforms of bounded functions. Our Tauberian theorem does not allow first-order poles on the imaginary axis, but any milder singularities, characterized by pseudofunction boundary behavior, are permissible. In this context we obtain a useful Tauberian theorem by exploiting Newman's `contour method'.

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BibTeXRIS

Jaap Korevaar. 2003-12-04. A Tauberian Theorem for Laplace Transforms with Pseudofunction Boundary Behavior. https://arxiv.org/abs/math/0312104

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