
Approximation of Additive Convolution-Like Operators
Real C*-Algebra Approach
Birkhäuser (Publisher)
Published on 16. May 2008
Book
Paperback/Softback
XII, 306 pages
978-3-7643-8750-1 (ISBN)
Description
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.
More details
Series
Edition
2008 ed.
Language
English
Place of publication
Basel
Switzerland
Publishing group
Springer Basel
Target group
Professional and scholarly
Research
Illustrations
XII, 306 p.
Dimensions
Height: 240 mm
Width: 170 mm
Thickness: 18 mm
Weight
552 gr
ISBN-13
978-3-7643-8750-1 (9783764387501)
DOI
10.1007/978-3-7643-8751-8
Schweitzer Classification
Other editions
Additional editions

Victor Didenko | Bernd Silbermann
Approximation of Additive Convolution-Like Operators
Real C*-Algebra Approach
E-Book
09/2008
1st Edition
Birkhäuser
€50.28
Available for download
Content
Complex and Real Algebras.- Approximation of Additive Integral Operators on Smooth Curves.- Approximation Methods for the Riemann-Hilbert Problem.- Piecewise Smooth and Open Contours.- Approximation Methods for the Muskhelishvili Equation.- Numerical Examples.