rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Approximation of Additive Convolution-Like Operators
    sub title: Real C*-Algebra Approach
  name:
    name part: Didenko, Victor D.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Silbermann, Bernd.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: sz
    date issued: 2008
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XII, 306 p. online resource.
  abstract: 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: 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.
  note: by Victor D. Didenko, Bernd Silbermann.
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Integral equations
  subject:
    topic: Integral transforms
  subject:
    topic: Operational calculus
  subject:
    topic: Operator theory
  subject:
    topic: Partial differential equations
  subject:
    topic: Numerical analysis
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Operator Theory
  subject:
    topic: Numerical Analysis
  subject:
    topic: Integral Equations
  subject:
    topic: Integral Transforms, Operational Calculus
  subject:
    topic: Partial Differential Equations
  classification: QA150-272
  classification: 512
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Frontiers in Mathematics
  identifier: 9783764387518
  identifier: http://dx.doi.org/10.1007/978-3-7643-8751-8
  record info:
    record creation date: 100301
    record change date: 20151204183035.0
    record identifier: 978-3-7643-8751-8