International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 60916, 6 pages
doi:10.1155/2007/60916
Research Article
A Finite-Interval Uniqueness Theorem for Bilateral Laplace Transforms
Department of Mathematics, Statistics and Computer Science, St. Francis Xavier University, Antigonish, NS, B2G 2W5, Canada
Received 23 June 2007; Accepted 30 September 2007
Academic Editor: Narendra Kumar K. Govil
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.
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.