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Related singular problems and the generalized Hilbert transform

Published online by Cambridge University Press:  14 February 2012

John W. Dettman
John W. Dettman
Affiliation:
Department of Mathematical Sciences, Oakland University, Rochester, Michigan, U.S.A.
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Synopsis

Abstract 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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 79 , Issue 1-2 , 1977 , pp. 173 - 182
Copyright
Copyright © Royal Society of Edinburgh 1977

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