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The Kontorovich–Lebedev transformation on distributions of compact support and its inversion†

Published online by Cambridge University Press:  24 October 2008

A. H. Zemanian
A. H. Zemanian
Affiliation:
State University of New York at Stony Brook
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Extract

1. During the past decade a variety of integral transformations have been extended to various classes of distributions. However, one important integral transformation, which has defied such generalization, is the Kontorovich–Lebedev transformation. The objective of this note is to alter that situation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 77 , Issue 1 , January 1975 , pp. 139 - 143
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

REFERENCES

(1)Lebedev, N. N.Sur une formule d'inversion. Dokl. Akad. Nauk SSSR (N.S.) 52 (1946), 655–658.Google Scholar
(2)Schwabtz, L.Théorie des distributions. Hermann; (Paris, 1966).Google Scholar
(3)Sneddon, I. N.The use of integral transforms. McGraw-Hill Book Co.; (New York, 1972).Google Scholar
(4)Zemanian, A. H.Generalized integral transformations. Interscience Publishers; (New York, 1968).Google Scholar