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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

References

1. Artin, M., Brauer-Severi varieties, in Brauer groups in ring theory and algebraic geometry, Springer LNM 917 (Springer-Verlag, Berlin, 1982).Google Scholar
2. Dieudonné, J., Sur une generalisation du group orthogonal a quatre variables, Archiv. der Math.(1948), 282–287.Google Scholar
3. Draxl, P.K., Skew fields (Cambridge University Press, Cambridge, 1983).Google Scholar
4. Heuser, A., Uber den Funktionenkorper der Normfiache einer zentral einfachen Algebra, J. Reine Angew. Math. 301 (1978), 105–113.Google Scholar
5. Jacobson, N., Structure groups and Lie algebras of Jordan algebras of symmetric elements of associative algebras with involution, Advance in Math. 20 (1976), 106–150.Google Scholar
6. Marcus, M. and Moyls, B.N., Linear transformations on algebras of matrices, Can. J. Math. 11 (1959), 61–66.Google Scholar
7. Roquette, P., On the Galois cohomology of the projective linear group and its applications to the construction of generic splitting field of algebras, Math. Ann. 150 (1962), 411—439.Google Scholar
8. Saltman, D., Norm polynomials and algebras, J. Algebra 62 (1980), 333–345.Google Scholar
9. Serre, J.P., Local fields, English translation, Springer GTM 67 (Springer-Verlag, New York, 1979).Google Scholar
10. Waterhouse, W.C., Linear maps preserving reduced norms, Linear Algebra and Its Appl. 43 (1982), 197–200.Google Scholar