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One-Dimensional Linear Singular Integral Equations I. Introduction

This book is an introduction to the theory of linear one-dimensional singular integral equations. It is essentually a graduate textbook. Singular integral equations have attracted more and more attention, because, on one hand, this class of equations appears in many applications and, on the other, i...

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Bibliographic Details
Main Authors: Gohberg, I., Krupnik, N. (Author)
Format: eBook
Language:English
Published: Basel Birkhäuser 1992, 1992
Edition:1st ed. 1992
Series:Operator Theory: Advances and Applications
Subjects:
Humanities And Social Sciences
Humanities
Social Sciences
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • Comments and references
  • 3 Singular integral operators with continuous coefficients
  • 3.1 The index of a continuous function
  • 3.2 Singular integral operators with rational coefficients
  • 3.3 Factorization of functions
  • 3.4 The canonical factorization in a commutative Banach algebra
  • 3.5 Proof of the factorization theorem
  • 3.6 The local factorization principle
  • 3.7 Operators with continuous coefficients
  • 3.8 Approximate solutions of singular integral equations
  • 3.9 Generalized factorizations of continuous functions
  • 3.10 Operators with continuous coefficients (continuation)
  • 3.11 Additional facts and generalizations
  • 3.12 Operators with degenerating coefficients
  • 3.13 A generalization of singular integral operators with continuous coefficients
  • 3.14 Solution of Wiener-Hopf equations
  • 3.15 Someapplications
  • 3.16 Exercises
  • Comments and references
  • 4 Fredholm operators
  • 4.1 Normally solvable operators
  • 4.2 The restriction of normally solvable operators
  • 4.3 Perturbation of normally solvable operators
  • 4.4 The normal solvability of the adjoint operator
  • 4.5 Generalized invertible operators
  • 4.6 Fredholm operators
  • 4.7 Regularization of operators. Applications to singular integral operators
  • 4.8 Index and trace
  • 4.9 Functions of Fredholm operators and their index
  • 4.10 The structure of the set of Fredholm operators
  • 4.11 The Dependence of kerX and imX on the operator X
  • 4.12 The continuity of the function kx
  • 4.13 The case of a Hilbert space
  • 4.14 The normal solvability of multiplication by a matrix function
  • 4.15 ?±-operators
  • 4.16 One-sided regularization of operators
  • 4.17 Projections of invertible operators
  • 4.18 Exercises
  • Comments and references
  • 5 Local Principles and their first applications
  • 5.1 Localizing classes
  • 5.2 Multipliers on
  • 5.3 paired equations with continuous coefficients on
  • 1 The operator of singular integration
  • 1.1 Notations, definitions and auxiliary statements
  • 1.2 The boundedness of the operator S? in the space Lp(?) with ? being a simple curve
  • 1.3 Nonsimple curves
  • 1.4 Integral operators in weighted Lp spaces
  • 1.5 Unbounded curves
  • 1.6 The operator of singular integration in spaces of Hölder continuous functions
  • 1.7 The operator S?*
  • 1.8 Exercises
  • Comments and references
  • 2 One-sided invertible operators
  • 2.1 Direct sum of subspaces
  • 2.2 The direct complement
  • 2.3 Linear operators. Notations and simplest classes
  • 2.4 Projectors connected with the operator of singular integration
  • 2.5 One-sided invertible operators
  • 2.6 Singular integral operators and related operators
  • 2.7 Examples of one-sided invertible singular integral operators
  • 2.8 Two lemmas on the spectrum of an element in a subalgebra of a Banach algebra
  • 2.9 Subalgebras of a Banach algebra generated by one element
  • 2.10 Exercises

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