On the inversion of the convolution and Laplace transform

Author:
Boris Baeumer

Journal:
Trans. Amer. Math. Soc. **355** (2003), 1201-1212

MSC (2000):
Primary 44A35, 44A10, 44A40

DOI:
https://doi.org/10.1090/S0002-9947-02-03174-4

Published electronically:
October 25, 2002

MathSciNet review:
1938753

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Abstract | References | Similar Articles | Additional Information

Abstract: We present a new inversion formula for the classical, finite, and asymptotic Laplace transform of continuous or generalized functions . The inversion is given as a limit of a sequence of finite linear combinations of exponential functions whose construction requires only the values of evaluated on a Müntz set of real numbers. The inversion sequence converges in the strongest possible sense. The limit is uniform if is continuous, it is in if , and converges in an appropriate norm or Fréchet topology for generalized functions . As a corollary we obtain a new constructive inversion procedure for the convolution transform ; i.e., for given and we construct a sequence of continuous functions such that .

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Additional Information

**Boris Baeumer**

Affiliation:
Department of Mathematics and Statistics, University of Otago, P.O. Box 56, Dunedin, New Zealand

Email:
bbaeumer@maths.otago.ac.nz

DOI:
https://doi.org/10.1090/S0002-9947-02-03174-4

Keywords:
Operational calculus,
generalized functions,
integral transforms.

Received by editor(s):
January 25, 1999

Received by editor(s) in revised form:
August 5, 2002

Published electronically:
October 25, 2002

Article copyright:
© Copyright 2002
American Mathematical Society