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Frontiers in Mathematics

Approximation of Additive Convolution-Like Operators

Real C*-Algebra Approach

Authors: Didenko, Victor, Silbermann, Bernd

  • Based on algebraic techniques
  • First book entirely devoted to numerical analysis for additive operators
  • Covers various aspects of approximation methods for equations with conjugation arising in the boundary integral equation method
  • First book to present systematic study of approximation methods for the Muskhelishvili equation
  • Self-contained and accessible to graduate students
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eBook $54.99
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  • ISBN 978-3-7643-8751-8
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Softcover $69.95
price for USA
  • ISBN 978-3-7643-8750-1
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  • Usually dispatched within 3 to 5 business days.
About this book

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 (6 chapters)

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-7643-8751-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.95
price for USA
  • ISBN 978-3-7643-8750-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Approximation of Additive Convolution-Like Operators
Book Subtitle
Real C*-Algebra Approach
Authors
Series Title
Frontiers in Mathematics
Copyright
2008
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-7643-8751-8
DOI
10.1007/978-3-7643-8751-8
Softcover ISBN
978-3-7643-8750-1
Series ISSN
1660-8046
Edition Number
1
Number of Pages
XII, 306
Topics