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On the and Transformations

Published online by Cambridge University Press:  20 November 2018

P. G. Rooney
P. G. Rooney*
Affiliation:
University of Toronto, Toronto, Ontario
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Denote by C0 the collection of complex-valued functions which are continuous and compactly supported on (0, ∞). The transformations of the title are defined on C0 by

1.1

and

1.2

respectively, where Yv(x) is the Bessel function of the second kind, and Hv(x) is the Struve function; see [1; 7.5.4(55)]. The two transformations are studied briefly in [6; §8.4]; tables of transform pairs are given in [2; Chapters IX and XI], where it is also stated that, for – , each of the transformations is the inverse of the other.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 5 , 01 October 1980 , pp. 1021 - 1044
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Erdélyi, A et al., Higher transcendental functions I and II (New York, 1953).Google Scholar
2. Erdélyi, A et al., Integral transforms, I and II. Google Scholar
3. Rooney, P. G., On the ranges of certain fractional integrals, Can. J. Math. 24 (1972), 1198–1216.Google Scholar
4. Rooney, P. G., A technique for studying the boundedness and extendability of certain types of operators, Can. J. Math. 25 (1973), 1090–1102.Google Scholar
5. Rooney, P. G., On the range of the Hankel transformation, Bull. Lond. Math. Soc. 11 (1979), 45–48.Google Scholar
6. Titchmarsh, E. C., Fourier integrals (Oxford, 1948).Google Scholar