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The n-Dimensional Hilbert Transform of Distributions, Its Inversion and Applications

Published online by Cambridge University Press:  20 November 2018

O. P. Singh  and
J. N. Pandey
O. P. Singh
Affiliation:
Banaras Hindu University, Varanasi, India
J. N. Pandey
Affiliation:
Carleton University, Ottawa, Ontario
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Pandey and Chaudhary [13] recently developed the theory of Hilbert transform of Schwartz distribution space (DLp)',p > 1 in one dimension using Parseval's types of relations for one dimensional Hilbert transform [17] and noted that their theory coincides with the corresponding theory for the Hilbert transform developed by Schwartz [16] by using the technique of convolution in one dimension.

The corresponding theory for the Hilbert transform in n-dimension is considerably harder and will be successfully accomplished in this paper.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 2 , 01 April 1990 , pp. 239 - 258
Copyright
Copyright © Canadian Mathematical Society 1990

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