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On a class of systems of singular integral equations on a bounded domain

Published online by Cambridge University Press:  14 November 2011

A. Džuraev
A. Džuraev
Affiliation:
Tajik Academy of Sciences, Leninski Prospect 33, 734025 Dushanbe, U.S.S.R.
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Synopsis

A class of systems of two-dimensional singular integral equations with even kernels over bounded domains in the plane is studied. The applications include integral equations with the Bergman kernel function. The method of investigation is the following: the integral equation is reduced to a Riemann type boundary value problem for a first order elliptic system. This is solved by means of one-dimensional singular integral equations over the boundary curve. An adjoint problem is formulated, the Noetherian theorems are established, and a formula for the index is given.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 83 , Issue 3-4 , 1979 , pp. 347 - 364
Copyright
Copyright © Royal Society of Edinburgh 1979

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