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Zeitschrift für Analysis und ihre Anwendungen


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Volume 27, Issue 3, 2008, pp. 339–352
DOI: 10.4171/ZAA/1359

Published online: 2008-09-30

Kernel Dimension of Singular Integral Operators with Piecewise Continuous Coefficients on the Unit Circle

A. Rogozhin[1] and Bernd Silbermann[2]

(1) Technische Universität Chemnitz, Germany
(2) Technische Universität Chemnitz, Germany

In this paper we propose a method to compute the kernel dimension of a Fredholm singular integral operator $aP+bQ$ with piecewise continuous coefficients $a, b.$ We show that the kernel dimension can be extracted from the singular value behavior of a polynomial collocation method. The results are illustrated by numerical experiments.

Keywords: Cauchy singular integral operators, kernel dimension, singular values, splitting property

Rogozhin A., Silbermann Bernd: Kernel Dimension of Singular Integral Operators with Piecewise Continuous Coefficients on the Unit Circle. Z. Anal. Anwend. 27 (2008), 339-352. doi: 10.4171/ZAA/1359