Approximation of Additive Convolution Like Operators Real C Algebra Approach 1st Edition by Victor Didenko, Bernd Silbermann ISBN 3764387513 9783764387518

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ISBN 10: 3764387513

ISBN 13: 9783764387518

Author: Victor Didenko, Bernd Silbermann 

Various aspects of numerical analysis for equations arising in boundary integral equation methods have been the subject of several books published in the last 15 years [95, 102, 183, 196, 198]. Prominent examples include various classes of o- dimensional singular integral equations or equations related to single and double layer potentials. Usually, a mathematically rigorous foundation and error analysis for the approximate solution of such equations is by no means an easy task. One reason is the fact that boundary integral operators generally are neither integral operatorsof the formidentity plus compact operatornor identity plus an operator with a small norm. Consequently, existing standard theories for the numerical analysis of Fredholm integral equations of the second kind are not applicable. In the last 15 years it became clear that the Banach algebra technique is a powerful tool to analyze the stability problem for relevant approximation methods [102, 103, 183, 189]. The starting point for this approach is the observation that the ? stability problem is an invertibility problem in a certain BanachorC -algebra. As a rule, this algebra is very complicated – and one has to ?nd relevant subalgebras to use such tools as local principles and representation theory. However,invariousapplicationsthereoftenarisecontinuousoperatorsacting on complex Banach spaces that are not linear but only additive – i. e. , A(x+y)= Ax+Ay for all x,y from a given Banach space. It is easily seen that additive operators 1 are R-linear provided they are continuous.

Table of contents:

Chapter 1. Complex and Real Algebras
Chapter 2. Approximation of Additive Integral Operators on Smooth Curves
Chapter 3. Approximation Methods for the Riemann–Hilbert Problem
Chapter 4. Piecewise Smooth and Open Contours
Chapter 5. Approximation Methods for the Muskhelishvili Equation
Chapter 6. Numerical Examples

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Tags: Victor Didenko, Bernd Silbermann, Approximation, Additive Convolution Like Operators, Real C Algebra Approach