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Numerical Analysis for Integral and Related Operator Equations
- Publisher
- de Gruyter
- Copyright
- Copyright © by Walter de Gruyter GmbH
- ISSN
- 1572-9176
- eISSN
- 1572-9176
- DOI
- 10.1515/GMJ.2000.633
- Publisher site
- See Article on Publisher Site
Abstract
AbstractWe prove the boundedness of the Cauchy singular integral operator in special weighted Sobolev and Hölder-Zygmund spaces for large values of the smoothness parameter, which is an integer m ≥ 0, when the underlying contour is piecewise-smooth with angular points and even with cusps. We obtain Fredholm criteria and an index formula for singular integral equations with piecewise-continuous coefficients and complex conjugation in the spaces and provided that the underlying contour has only angular points but no cusps. The Fredholm property and the index turn out to be independent of the smoothness parameter m.
Journal
Georgian Mathematical Journal – de Gruyter
Published: Dec 23, 2000