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International Journal of Mathematics and Mathematical Sciences
Volume 8, Issue 2, Pages 325-344
http://dx.doi.org/10.1155/S0161171285000345

Analytic representation of the distributional finite Hankel transform

1Department of Mathematics, Banaras Hindu University, Varanasi 221005, India
2Department of Mathematics, Faculty of Science, King Saud University, Riyadh, Saudi Arabia

Received 30 April 1983

Copyright © 1985 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Various representations of finite Hankel transforms of generalized functions are obtained. One of the representations is shown to be the limit of a certain family of regular generalized functions and this limit is interpreted as a process of truncation for the generalized functions (distributions). An inversion theorem for the gereralized finite Hankel transform is established (in the distributional sense) which gives a Fourier-Bessel series representation of generalized functions.