Approximation of additive convolution-like operators: Real C-star-algebra approach

✍ Scribed by Didenko V., Silbermann B.

• Publisher: Birkhauser
• Year: 2008
• Tongue: English
• Leaves: 320
• Series: Frontiers in Mathematics
• Category: Library

✦ Synopsis

This book deals with numerical analysis for certain classes of additive operators and related equations, including singular integral operators with conjugation, the Riemann-Hilbert problem, Mellin operators with conjugation, double layer potential equation, and the Muskhelishvili equation. The authors propose a unified approach to the analysis of the approximation methods under consideration based on special real extensions of complex C*-algebras. The list of the methods considered includes spline Galerkin, spline collocation, qualocation, and quadrature methods. The book is self-contained and accessible to graduate students.

✦ Table of Contents

Cover......Page 1
Frontiers in Mathematics......Page 3
Approximation
of
Additive
Convolution-Like
Operators......Page 4
ISBN 9783764387501......Page 5
Contents......Page 6
Preface......Page 10
1
Complex and Real Algebras......Page 15
2
Approximation of Additive
Integral Operators on Smooth
Curves......Page 73
3
Approximation Methods for the
Riemann-Hilbert Problem......Page 137
4
Piecewise Smooth and Open
Contours......Page 171
5
Approximation Methods for the
Muskhelishvili Equation......Page 247
6
Numerical Examples......Page 289
Bibliography......Page 299
Index......Page 317