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A distributional Hardy transformation

Published online by Cambridge University Press:  24 October 2008

R. S. Pathak  and
J. N. Pandey
R. S. Pathak
Affiliation:
Department of Mathematics, Banaras Hindu University, Varanasi (U.P.), India and Carleton University, Ottawa, Ontario, Canada
J. N. Pandey
Affiliation:
Department of Mathematics, Banaras Hindu University, Varanasi (U.P.), India and Carleton University, Ottawa, Ontario, Canada
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Extract

In this paper the classical Hardy transformation (5) has been extended to distributions. The celebrated Hankel transformation, Y-transformation and H-transformation are particular cases of the Hardy transformation. The Hankel transformation has been extended to distributions by Zemanian(12). The distributional theory has been explored by Zemanian(13), Koh and Zemanian(6), and Dubey and Pandey(2). The famous Y- and its reciprocal H-transformations have not been extended to distributions. The inversion and some of the properties of these distributional transformations can be deduced as particular cases of the results contained in this paper.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 76 , Issue 1 , July 1974 , pp. 247 - 262
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

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