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Spectral Theory of Approximation Methods for Convolution Equations

  • Book
  • © 1995

Overview

Authors:
  1. Roland Hagen

    1. Facultät für Mathematik, Technische Universität Chemnitz-Zwickau, Chemnitz, Germany

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  2. Steffen Roch

    1. Facultät für Mathematik, Technische Universität Chemnitz-Zwickau, Chemnitz, Germany

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  3. Bernd Silbermann

    1. Facultät für Mathematik, Technische Universität Chemnitz-Zwickau, Chemnitz, Germany

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Part of the book series: Operator Theory: Advances and Applications (OT, volume 74)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-XII
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  2. Invertibility in Banach algebras

    • Roland Hagen, Steffen Roch, Bernd Silbermann
    Pages 1-43

  3. Spline spaces and Toeplitz operators

    • Roland Hagen, Steffen Roch, Bernd Silbermann
    Pages 45-144

  4. Algebras of spline approximation sequences

    • Roland Hagen, Steffen Roch, Bernd Silbermann
    Pages 145-224

  5. Singularities

    • Roland Hagen, Steffen Roch, Bernd Silbermann
    Pages 225-280

  6. Manifolds

    • Roland Hagen, Steffen Roch, Bernd Silbermann
    Pages 281-336

  7. Around finite sections of integral operators

    • Roland Hagen, Steffen Roch, Bernd Silbermann
    Pages 337-355

  8. Back Matter

    Pages 357-373
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Keywords

About this book

The aim of the present book is to propose a new algebraic approach to the study of norm stability of operator sequences which arise, for example, via discretization of singular integral equations on composed curves. A wide variety of discretization methods, including quadrature rules and spline or wavelet approximations, is covered and studied from a unique point of view. The approach takes advantage of the fruitful interplay between approximation theory, concrete operator theory, and local Banach algebra techniques. The book is addressed to a wide audience, in particular to mathematicians working in operator theory and Banach algebras as well as to applied mathematicians and engineers interested in theoretical foundations of various methods in general use, particularly splines and wavelets. The exposition contains numerous examples and exercises. Students will find a large number of suggestions for their own investigations.

Authors and Affiliations

  • Facultät für Mathematik, Technische Universität Chemnitz-Zwickau, Chemnitz, Germany

    Roland Hagen, Steffen Roch, Bernd Silbermann

Bibliographic Information

  • Book Title: Spectral Theory of Approximation Methods for Convolution Equations

  • Authors: Roland Hagen, Steffen Roch, Bernd Silbermann

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-0348-9067-0

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Verlag 1995

  • Hardcover ISBN: 978-3-7643-5112-0Due: 01 September 1994

  • Softcover ISBN: 978-3-0348-9891-1Published: 20 September 2011

  • eBook ISBN: 978-3-0348-9067-0Published: 06 December 2012

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: 376

  • Topics: Numerical Analysis, Analysis

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