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# Singular Integral Operators by Siegfried Prossdorf, Solomon G. Mikhlin (Paperback, 2013)

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## About this product

### Key Features

- Author(s)Siegfried Prossdorf,Solomon G. Mikhlin
- PublisherSpringer-Verlag Berlin and Heidelberg GmbH & Co. KG
- Date of Publication24/07/2013
- Language(s)English
- FormatPaperback
- ISBN-103642648924
- ISBN-139783642648922
- GenreMathematics

### Publication Data

- Place of PublicationBerlin
- Country of PublicationGermany
- ImprintSpringer-Verlag Berlin and Heidelberg GmbH & Co. K
- Content Notebiography

### Dimensions

- Weight807 g
- Width155 mm
- Height235 mm
- Spine27 mm
- Pagination528

### Credits

- Translated byA. Bottcher,R. Lehmann

### Editorial Details

- Edition StatementSoftcover reprint of the original 1st ed. 1986

### Description

- Table Of ContentsI. Basic facts from functional analysis.- 1. Basic concepts.- 2. Regularizatlon of operators.- 3. Fredholm and semi-Fredholm operators on Banach spaces.- 4. Fredholm and semi-Fredholm operators on linear topological spaces.- 5. The symbol.- 6. The symbol of the convolution operator.- II. The one-dimensional singular integral.- 1. The singular integral and its simplest properties.- 2. The boundedness of the singular integral operator on the space Lp(?).- 3. The boundedness of the singular integral operator on the space Lp with weight.- 4. Further properties of the singular integral operator.- 4.1. Integral operators with weak singularity.- 4.2. Two theorems on commutators.- 4.3. The Poincare-Bertrand commutation formula.- 4.4. The singular integral operator on the space H?(?).- 5. Operators related to the Cauchy singular integral.- 5.1. The adjoint singular integral operator.- 5.2. The singular integral with Hilbert kernel.- 5.3. The projections generated by the singular integral.- 6. The singular integral operator on spaces of differentiable functions.- III. One-dimensional singular integral equations with continuous coefficients on closed curves.- 1. Abstract singular operators.- 1.1. Paired operators.- 1.2. Abstract singular operators.- 2. Singular integral operators with rational coefficients.- 3. Singular integral operators with continuous coefficients.- 4. Singular integral operators on the space H?(?).- 5. Factorization of continuous functions.- 5.1. Factorization in R-algebras.- 5.2. Factorization in algebras with two norms.- 6.3. Generalized factorization of continuous functions.- 6. Effective solution of singular integral equations with continuous coefficients.- 7. The case of a composite curve system.- IV. One-dimensional singular integral equations with discontinuous coefficients.- 1. Preliminaries.- 1.1. Alteration of the integration curve.- 1.2. Separation of the singularities.- 2. Singular equations with bounded measurable coefficients.- 2.1. Necessary conditions for the Fredholm property.- 2.2. Theorems on the kernel and cokernel.- 2.3. Reduction to the case of an invertible operator.- 3. Generalized factorization of bounded measurable functions and the effective solution singular equations.- 3.1. Generalized factorization in the space Lp(?, ?).- 3.2. Effective solution of singular equations with bounded measurable coefficients.- 4. Singular equations with piecewise continuous coefficients on closed curves.- 5. Singular equations with piecewise continuous coefficients on non-closed curves.- 6. Singular equations with piecewise continuous coefficients on the real line.- 7. Norm estimates for the singular integral operator.- V. Systems of one-dimensional singular equations.- 1. Two theorems on operator matrices.- 2. Systems of singular integral equations with continuous coefficients on closed curves.- 3. Factorization of matrix functions.- 3.1. General factorization theorems.- 3.2. Canonical factorization of matrix functions.- 4. Generalized factorization of continuous matrix functions and its application.- 5. Systems of singular integral equations with bounded measurable coefficients.- 6. Systems of singular integral equations with piecewise continuous coefficients.- 6.1. The case of closed curves.- 6.2. The case of non-closed curves.- 6.3. The definition of the symbol.- 7. Productsums of singular operators with piecewise continuous coefficients.- 8. The algebra generated by singular operators with piecewise continuous coefficients.- VI. One-dimensional singular equations with degenerate symbol.- 1. Reduction of an operator with finite index to a Fredholm operator.- 2. Factorization of abstract singular operators.- 3. Some classes of differentiable functions.- 4. Function spaces.- 5. Singular operators with degenerate continuous coefficients.- 6. Singular operators with degenerate piecewise continuous coefficients.- 7. Singular oper

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