Stabilitätskriterien für Näherungsverfahren bei singulären Integralgleichungen in $L^p$

Abstract

Approximation methods for one-dimensional singular integral equations with piecewise continuous coefficients on simple closed Liapunov curves are considered. For spline Calerkin methods and for spline and trigonometric collocation, necessary and sufficient conditions for their stability in $L^p$ are given. The central idea is a general stability criterion for sequences of approximate operators with circulant structure.