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A Mixed Parseval's Equation And a Generalized Hankel Transformation of Distributions

Published online by Cambridge University Press:  20 November 2018

J. J. Betancor
J. J. Betancor*
Affiliation:
University of La Laguna, La Laguna, Canary Islands
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Let an integral transform T﹛f﹜ of a complex valued function f(x) defined over the interval (0, ∞) be defined as One of the most usual procedures to extend the classical transform (l.a) to generalized functions consists in constructing a space A of testing functions over (0, ∞) which is closed with respect to the classical transform (l.a) and then the corresponding transform of the generalized function/ of the dual space of A is defined through

This approach has been followed by L. Schwartz [13] and A. H. Zemanian [20], amongst others.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 41 , Issue 2 , 01 April 1989 , pp. 274 - 284
Copyright
Copyright © Canadian Mathematical Society 1989

References

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