Spectral Theory of Approximation Methods for Convolution Equations

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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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.

• Banach algebra
• C*-algebra
• Operator theory
• Singular integral
• convolution

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

  Roland Hagen, Steffen Roch, Bernd Silbermann

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