A Tauberian Theorem for Laplace Transforms with Pseudofunction Boundary Behavior
Classical Analysis and ODEs
2007-05-23 v1 Complex Variables
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'.
Cite
@article{arxiv.math/0312104,
title = {A Tauberian Theorem for Laplace Transforms with Pseudofunction Boundary Behavior},
author = {Jaap Korevaar},
journal= {arXiv preprint arXiv:math/0312104},
year = {2007}
}
Comments
11 pages, 1 figure