IJPAM: Volume 56, No. 1 (2009)


Claudiu Mihai
4380, Main Street
Amherst, NY 14226, USA
e-mail: [email protected]

Abstract.In this paper we discus the zeros of analytic functions that admit a Laplace transform represention. In particular, we complement a classical result of Yu-Cheng Shen from 1947 by showing that for all sequences $\lambda_n\in\C$ with $Re\lambda_n \ge \gamma > 0$ and $\left\vert\arg(\la_n)\right\vert\leq \theta<\frac{\pi}{2}$ for all $n\in \N$ and $\sum^{\infty}_{n=1}1-\frac{\left\vert\lambda_n-1\right\vert}{\left\vert\lambda_n+1\right\vert} < \infty$, there exists $0\not= f \in L^1_{loc}[0,\infty)$ such that the Laplace transform $\hat{f}$ exists for $Re\lambda > \gamma$ and satisfies $\hat{f}(\lambda_n) = 0$ for all $n\in \N$.

Received: July 22, 2009

AMS Subject Classification: 44A10

Key Words and Phrases: Laplace transform, uniqueness sequences

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 56
Issue: 1