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Laplace Transforms and Generalized Laguerre Polynomials

Published online by Cambridge University Press:  20 November 2018

P. G. Rooney
P. G. Rooney*
Affiliation:
University of Toronto
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Various sets of necessary and sufficient conditions are known in order that a function ƒ(s), analytic for Re s > 0, be represented as the Laplace transform of a function in Lp(0,∞), 1 < p ⩽ ∞ . Most of these theories are based on the properties of some inversion operator for the transformation— see, for example, (7, chap. 7). However in the case p = 2 a number of representation theorems of a much simpler type are available.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 177 - 182
Copyright
Copyright © Canadian Mathematical Society 1958

References

1. Doetsch, G., Handbuch der Laplace Transformation I (Basel, 1950).Google Scholar
2. Erdélyi, A. et al., Higher Transcendental Functions II (New York, 1953).Google Scholar
3. Erdélyi, A. et al., Tables of Integral Transforms I (New York, 1954).Google Scholar
4. Rooney, P. G., On an inversion formula for the Laplace transformation, Can. J. Math., 7 (1955), 101–115.Google Scholar
5. Shohat, J., Laguerre polynomials and the Laplace transform, Duke Math. J., 6 (1940), 615–626.Google Scholar
6. Titchmarsh, E. C., Introduction to the Theory of Fourier Integrals (Oxford, 1948).Google Scholar
7. Widder, D. V., The Laplace Transform (Princeton, 1941).Google Scholar