Geodesic
The n-Dimensional Hilbert Transform of Distributions, Its Inversion and Applications
Canadian journal of mathematics, Tome 42 (1990) no. 2, pp. 239-258

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Singh, O. P.; Pandey, J. N. The n-Dimensional Hilbert Transform of Distributions, Its Inversion and Applications. Canadian journal of mathematics, Tome 42 (1990) no. 2, pp. 239-258. doi: 10.4153/CJM-1990-014-4
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[1] 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] 2. Dieudonné, J., Sur une generalisation du group orthogonal a quatre variables, Archiv. der Math.(1948), 282–287. Google Scholar

[3] 3. Draxl, P.K., Skew fields (Cambridge University Press, Cambridge, 1983). Google Scholar

[4] 4. Heuser, A., Uber den Funktionenkorper der Normfiache einer zentral einfachen Algebra, J. Reine Angew. Math. 301 (1978), 105–113. Google Scholar

[5] 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] 6. Marcus, M. and Moyls, B.N., Linear transformations on algebras of matrices, Can. J. Math. 11 (1959), 61–66. Google Scholar

[7] 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] 8. Saltman, D., Norm polynomials and algebras, J. Algebra 62 (1980), 333–345. Google Scholar

[9] 9. Serre, J.P., Local fields, English translation, Springer GTM 67 (Springer-Verlag, New York, 1979). Google Scholar

[10] 10. Waterhouse, W.C., Linear maps preserving reduced norms, Linear Algebra and Its Appl. 43 (1982), 197–200. Google Scholar

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