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Spectral Theory of Approximation Methods for Convolution Equations

  • Roland Hagen
  • Steffen Roch
  • Bernd Silbermann

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

Table of contents

  1. Front Matter
    Pages I-XII
  2. Roland Hagen, Steffen Roch, Bernd Silbermann
    Pages 1-43
  3. Roland Hagen, Steffen Roch, Bernd Silbermann
    Pages 45-144
  4. Roland Hagen, Steffen Roch, Bernd Silbermann
    Pages 145-224
  5. Roland Hagen, Steffen Roch, Bernd Silbermann
    Pages 225-280
  6. Roland Hagen, Steffen Roch, Bernd Silbermann
    Pages 281-336
  7. Roland Hagen, Steffen Roch, Bernd Silbermann
    Pages 337-355
  8. Back Matter
    Pages 357-373

About this book

Introduction

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.

Keywords

Banach algebra C*-algebra Operator theory Singular integral convolution

Authors and affiliations

  • Roland Hagen
    • 1
  • Steffen Roch
    • 1
  • Bernd Silbermann
    • 1
  1. 1.Facultät für MathematikTechnische Universität Chemnitz-ZwickauChemnitzGermany

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