Equations with involutive operators具对合算子的方程
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作者： Nikolai Karapetiants，Stefan Samko著
出 版 社：
出版时间： 2001-6-1字数：版次： 1页数： 427印刷时间： 2001/06/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780817641573包装： 精装内容简介
Equations with Involutive Operators demonstrates an important interplay between abstract and concrete operator theory。The focus is on the investigation of a number of equations，which，while seemingly different，are all unified by the same idea：they are all realizations of some operator equations in Banach spaces。One permeating theme in these equations involves the role of the Fredholm property。The text is carefully written，self-contained，and covers a broad range of topics and results。Key ideas are developed in a step-by step approach，beginning with required background and historical material，and culminating in the final chapters with state-of-the art topics。Experts in operator theory，integral equations，and function theory as well as students in these areas will find open problems for further investigations。The book will also be useful to engineers using operator theory and integral equation techniques。Good examples，bibliography and index make this text a valuable classroom or reference resource。
目录
Table of Contents
Introduction
Notation
1 On Fredholmness of Singular Type Operators
1 Fredholm operators
2 Singular integral operators with piecewise continuous coefficients in the space L〔subscript p〕（〔gamma〕）
3 On Fredholmness of convolution type operators
4 Bibliographic notes to Chapter 1
2 On Fredholmness of Other Singular-type Operators
5 On operators with homogeneous kernels； the one-dimensional case
6 Operators with homogeneous kernels； the multi-dimensional case
7 Convolution-type operators with discontinuous symbols
8 Bibliographic notes to Chapter 2
3 Functional and Singular Integral Equations with Carleman Shifts in the Case of Continuous Coefficients
9 Carleman and generalized Carleman shifts
10 A functional equation with shift
11 Singular integral equations with Carleman shift on a closed curve； the case of continuous coefficients
12 Singular integral equations with Carleman shift on an open curve； the case of continuous coefficients
13 Bibliographic notes to Chapter 3
4 Two-term Equations （A+QB）〔phi〕 = f with an Involutive Operator Q； an Abstract Approach and Applications
14 Fredholmness of an abstract equation with an involutive operator； non-matrix approach
15 Application to singular integral equations with complex conjugate unknowns
16 Applications to integral equations on the real line with reflection or inversion
17 Application to singular integral equations with Carleman shift on an open curve； the case of discontinuous coefficients
18 Singular integral equations with a fractional linear shift in the space L〔superscript p〕 with a special weight
19 Fredholmness of abstract equations with a generalized involutive operator （non-matrix approach）
20 Abstract equations with algebraic operators
21 Bibliographic notes to Chapter 4
5 Equations with Several Generalized Involutive Operators, Matrix Abstract Approach and Applications
22 Fredholmness of abstract equations with generalized involutive operators （matrix approach）
23 Singular integral equations with a finite group of shifts in the case of continuous coefficients
24 Singular integral equations with a finite group of shifts （the case of piecewise continuous coefficients）
25 Convolution type equations with shifts and complex conjugation 261
26 Bibliographic notes to Chpater 5
6 Application of the Abstract Approach to Singular Equation on the Real Line with Fractional Linear Shift
27 Singular integral operators perturbed by integral operators with homogeneous kernels
28 Singular integral operators with a fractional linear Carleman shift in the weighted space L〔subscript p〕〔superscript 〔gamma〕〕 （R〔superscript 1〕）
29 Equations including operators with homogeneous kernels, the singular integral operators and the inversion shift
30 Potential type operators on the real line with a fractional linear Carleman shift
31 Generalized Carleman fractional linear shifts on the real line
32 Singular integral equations with a generalized Carleman fractional linear shift
33 Bibliographic Notes to Chapter 6
7 Application to Hankel Type and Multidimensional Integral Equations
34 Convolution integral equations of Hankel type
35 Some multidimensional singular type equations with shifts
36 Bibliographic Notes to Chapter 7
Bibliography
Index
List of Symbols
