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Laplace Transformations of Distributions

Published online by Cambridge University Press:  20 November 2018

J. L. B. Cooper
J. L. B. Cooper*
Affiliation:
University of Toronto
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In a previous paper (2), I discussed conditions in order that a holomorphic function f(w) be a Laplace transform of a function F(t) such that, for some a, F(t)e-at ∈ Lp(0, ∞). These conditions involved (a) the behaviour of integral transforms of the values of the function on a vertical line w = const, and (b) conditions involving the order of magnitude of the function at infinity. The present article discusses the corresponding question for Laplace transforms of distributions.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 1325 - 1332
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Berens, H. and Butzer, P. L., Über die Darstellung vektorwertigen holomorpher Funktionen durch Laplace-Integrale, Math. Ann., 158 (1965), 269–283.Google Scholar
2.J. Cooper, L. B., The representation of functions as Laplace Transforms, Math. Ann., 159 (1965), 223–233.Google Scholar
3. Pólya, G. and Szegö, G., Aufgaben und Lehrsätze aus der Analysis, Vol. 1 (Berlin, 1925).Google Scholar
4. Schwartz, L., Théorie des distributions, Vol. 11 (Paris, 1951).Google Scholar
5. Schwartz, L., Transformation de Laplace des distributions, Medd. Lunds Mat. Sem. Supplementband (1952), 196–206.Google Scholar