A Finite-Interval Uniqueness Theorem for Bilateral Laplace Transforms

Chareka, Patrick

doi:https://doi.org/10.1155/2007/60916

International Journal of Mathematics and Mathematical Sciences

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Research Article | Open Access

Volume 2007 | Article ID 060916 | https://doi.org/10.1155/2007/60916

A Finite-Interval Uniqueness Theorem for Bilateral Laplace Transforms

Patrick Chareka¹

Academic Editor: Narendra Kumar K. Govil

Received23 Jun 2007

Accepted30 Sept 2007

Published04 Dec 2007

Abstract

Two or more bilateral Laplace transforms with a complex argument “s” may be equal in a finite vertical interval when, in fact, the transforms correspond to different functions. In this article, we prove that the existence of a bilateral Laplace transform in any finite horizontal interval uniquely determines the corresponding function. The result appears to be new as we could not find it in the literature. The novelty of the result is that the interval need not contain zero, the function need not be nonnegative and need not be integrable. The result has a potential to be useful in the context of fitting probability distributions to data using Laplace transforms or moment generating functions.

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Copyright

Copyright © 2007 Patrick Chareka. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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