Related singular problems and the generalized Hilbert transform
1977 ◽
Vol 79
(1-2)
◽
pp. 173-182
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Keyword(s):
SynopsisAbstract versions of the Cauchy problem for the Euler-Poisson-Darboux equation and the Dirichlet problem for the equation of generalized axially symmetric potential theory are related by an integral transformation. In certain special cases, this leads to abstract versions of (1) the Poisson formula for the solution of G.A.S.P.T. in a half-space, (2) pseudo-analytic functions in a half-space, and (3) a generalized Hilbert transform related to the work of Heywood, Kober, and Okikiolu. Some properties of this generalized Hilbert transform are studied including an inversion theorem.
2015 ◽
Vol 2015
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pp. 1-15
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Keyword(s):
2004 ◽
Vol 35
(6)
◽
pp. 1636-1643
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2018 ◽
Vol 24
(5)
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pp. 1425-1437
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2001 ◽
Vol 38
(32-33)
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pp. 5527-5543
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