In this paper we propose a method to compute the kernel dimension of a Fredholm singular integral operator with piecewise continuous coefficients 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.
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A. Rogozhin, Bernd Silbermann, Kernel Dimension of Singular Integral Operators with Piecewise Continuous Coefficients on the Unit Circle. Z. Anal. Anwend. 27 (2008), no. 3, pp. 339–352DOI 10.4171/ZAA/1359