A Tauberian Theorem for Laplace Transforms with Pseudofunction Boundary Behavior

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dc.creatorKorevaar, Jaap
dc.date2003-12-04
dc.date.accessioned2026-07-07T05:03:33Z
dc.date.available2026-07-07T05:03:33Z
dc.descriptionThe 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'.
dc.description11 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/math/0312104
dc.identifierhttp://arxiv.org/abs/math/0312104
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69467
dc.subjectClassical Analysis and ODEs
dc.subjectComplex Variables
dc.subjectPrimary: 40E05; Secondary: 11M45, 11N05, 42A38, 44A10, 46F20
dc.titleA Tauberian Theorem for Laplace Transforms with Pseudofunction Boundary Behavior
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