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Methods for solving a singular integral equation with Cauchy kernel on the real line

Methods for solving a singular integral equation with Cauchy kernel on the real line We study exact and approximate methods for solving a singular integral equation with Cauchy kernel on the real line. On the basis of the theory of positive operators, we prove an existence and uniqueness theorem for this equation in the space of Lebesgue square integrable functions. This theorem is then used to give a theoretical justification of general projection and projection-iteration methods as well as an iteration method for solving this equation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Methods for solving a singular integral equation with Cauchy kernel on the real line

Differential Equations , Volume 44 (7) – Sep 27, 2008

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References (15)

Publisher
Springer Journals
Copyright
Copyright © 2008 by MAIK Nauka
Subject
Mathematics; Difference and Functional Equations; Partial Differential Equations; Ordinary Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266108070100
Publisher site
See Article on Publisher Site

Abstract

We study exact and approximate methods for solving a singular integral equation with Cauchy kernel on the real line. On the basis of the theory of positive operators, we prove an existence and uniqueness theorem for this equation in the space of Lebesgue square integrable functions. This theorem is then used to give a theoretical justification of general projection and projection-iteration methods as well as an iteration method for solving this equation.

Journal

Differential EquationsSpringer Journals

Published: Sep 27, 2008

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