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On the Watson and Laplace Transformations

Published online by Cambridge University Press:  20 November 2018

P. G. Rooney  and
C. Schubert
P. G. Rooney
Affiliation:
University of Toronto
C. Schubert
Affiliation:
University of Toronto
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Extract

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Let k be the kernel of a Watson transformation; that is k(x)/x ϵ L2(0,∞), and if x and y are positive,

1

Then if g is the transform of F ϵ L2(0,∞), that is if

2

it i s known that g 2(0,∞), that

3

and that

4

For these results see [1; theorem 79].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 3 , Issue 3 , 01 September 1960 , pp. 247 - 253
Copyright
Copyright © Canadian Mathematical Society 1960

References

1. Bochner, S. and Chandrasekharan, K., Fourier Transforms, (Princeton, 1949).Google Scholar
2. Doetsch, G., Handbuch der Laplace Transformation I, (Basel, 1950).Google Scholar
3. Erdélyi, A. et al., Tables of Integral Transforms I, (New York, 1954).Google Scholar
4. Rooney, P. G., On some theorems of Doetsch, Canad. J. Math. 10 (1958), 421-430.Google Scholar
5. Rooney, P. G., On the inversion of general transformations, Canad. Math. Bull. 2 (1959) 19-24.Google Scholar