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Produktbild: Singular Integral Operators

Singular Integral Operators

Fr. 182.00

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Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

01.01.1987

Abbildungen

11 Abbildungen

Verlag

Springer Berlin

Seitenzahl

528

Maße (L/B/H)

24.9/17.4/3.4 cm

Gewicht

2020 g

Auflage

1986. 1986

Übersetzt von

A. Böttcher + weitere

Sprache

Englisch

ISBN

978-3-540-15967-4

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

01.01.1987

Abbildungen

11 Abbildungen

Verlag

Springer Berlin

Seitenzahl

528

Maße (L/B/H)

24.9/17.4/3.4 cm

Gewicht

2020 g

Auflage

1986. 1986

Übersetzt von

  • A. Böttcher
  • R. Lehmann

Sprache

Englisch

ISBN

978-3-540-15967-4

Herstelleradresse

Springer-Verlag GmbH
Heidelberger Platz 3
14197 Berlin
Deutschland
Email: sdc-bookservice@springer.com
Url: www.springer.com
Telephone: +49 6221 3454301
Fax: +49 30 8214091

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  • Produktbild: Singular Integral Operators
  • I. 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 Poincaré-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 operators with degenerate coefficients on non-closed curves.-
    8. Singular operators with degenerate measurable coefficients.-
    9. Singular matrix operators with degenerate coefficients.-
    10. Singular operators on the spaces C?(?) and C??(?).-
    11. Singular matrix operators with degenerate coefficients of constant rank.- VII. Some problems leading to singular integral equations.-
    1. Singular integro-differential equations.-
    2. The generalized Riemann-Hilbert-Poincaré problem.-
    3. A boundary value problem for elliptic systems of first order in the plane.-
    4. On algebraic operators.-
    5. Singular integral equations with Carleman shift.-
    6. The Tricomi equation.- VIII. Some further subsidiaries.-
    1. Stereographic projection.-
    2. Some function spaces.-
    3. Weakly singular integral operators.-
    4. On the powers of the Beltrami operator.- IX. Singular integrals of higher dimensions in spaces with a uniform metric.-
    1. Basic notions.-
    2. Singular integrals over an arbitrary integration manifold.-
    3. The Zygmund inequality.-
    4. Consequences of the Zygmund inequality.-
    5. The order of a singular integral at infinity.-
    6. Singular integrals in some other spaces with a uniform metric.- X. The symbol of higher dimensional singular integral operators.-
    1. The Fourier transform of a singular kernel. The symbol.-
    2. Expansion of the symbol into a series with respect to spherical functions.-
    3. Transformation of the symbol under a substitution of variables.-
    4. Transformation of the symbol under inversion.-
    5. A theorem on the boundedness of the singular operator.-
    6. On series with respect to spherical functions.-
    7. Differentiability properties of the symbol and the characteristic.-
    8. The symbol ring.- XI. Singular integral operators in spaces with integral metric.-
    1. An extension of the notion of a singular integral.-
    2. Criteria for boundedness in L2(Rm).-
    3. The theorem of Calderón and Zygmund.-
    4. Some further results.-
    5. Singular integrals in weighted spaces. Stein’s theorem.-
    6. Singular integrals in weighted spaces. The theorems of Plamenevski and Haikin.-
    7. A multiplication rule for symbols.-
    8. The adjoint singular operator.-
    9. Singular operators in Sobolev spaces.-
    10. Factor ring of singular operators.-
    11. Higher derivatives of the volume potential.-
    12. Weighted norm inequalities for maximal functions and singular integral operators.- XII. Multidimensional singular integral equations.-
    1. The constant symbol case.-
    2. The general case and Noether theorems.-
    3. Equivalent regularization. The index theorem.-
    4. A necessary condition for the existence of a regularizer.-
    5. Singular equations in Sobolev spaces.-
    6. Singular equations in test and in distribution spaces.-
    7. Polysingular integral operators.-
    8. Pseudo-differential operators.- XIII. Singular equations on smooth manifolds without boundary.-
    1. Manifolds.-
    2. Singular operators on manifolds. The symbol.-
    3. Singular equations in Lp(?).-
    4. On the gradient of a harmonic function.-
    5. The oblique derivative problem.-
    6. On the boundedness of singular operators in Lipschitz spaces.-
    7. Singular integral equations in Lipschitz spaces.- XIV. Systems of multidimensional singular equations.-
    1. General remarks.-
    2. The index problem. Reduction to a more special case.-
    3. Computation of the index.-
    4. The case of a two-dimensional manifold.-
    5. Elementary cases with index zero.-
    6. Problems in static elasticity theory.- XV. The localization principle. Singular operators on manifolds with boundary.-
    1. Operators of local type.-
    2. Equivalence at a point and locally Fredholm operators.-
    3. The envelope of an operator family.-
    4. A theorem on the connection between Fredholm and locally Fredholm operators.-
    5. Homogeneous operators and translation invariant operators.-
    6. Canonical singular integrals with piecewise continuous symbols.-
    7. Generalized singular integrals.-
    8. Compound generalized singular operators.-
    9. Singular integral equations in domains with boundary.-
    10. A survey on the papers by Vishik and Eskin.- XVI. Multidimensional singular equations with degenerate symbol.-
    1. Convolution equations with degenerate symbol.- 1.1. Function spaces.- 1.2. Existence and general form of the solution of the singular integral equation.- 1.3. A correctly posed problem.-
    2. Further results on convolution operators with degenerate symbol.-
    3. A multidimensional analogue of the Cauchy singular integral operator and the corresponding paired operators.- 3.1. Generalized Cauchy-Riemann systems.- 3.2. A generalized Borel-Pompeiu formula.- 3.3. Further properties of the singular integral operator S.- 3.4. Fredholm properties of certain degenerate paired operators.- 3.5. Some generalizations.- XVII. Methods for the approximate solution of one-dimensional singular integral equations.-
    1. General theorems on the convergence of projection methods.-
    2. Projection methods for the solution of abstract singular equations.-
    3. Polynomial approximation methods for the solution of singular integral equations.- 3.1. The reduction method.- 3.2. The collocation method.- 3.3. The method of mechanical quadratures.- 3.4. The method of least squares.- 3.5. The case of a non-vanishing index.- 3.6. Discontinuous coefficients.- 3.7. Singular integral equations over an interval.-
    4. Spline approximation methods for the solution of singular integral equations.- 4.1. The polygonal method.- 4.2. Collocation methods with splines of arbitrary degree.- 4.3. The Galerkin method.- 4.4. Singular integral equations over an interval.-
    5. The approximate solution of singular integral equations with degenerate symbol.- 6.1. The reduction method.- 5.2. The collocation method.- 5.3. The method of mechanical quadratures.- 5.4. The method of least squares.-
    6. The approximate solution of systems of singular integral equations.- 6.1. Polynomial approximation methods.- 6.2. Discontinuous coefficients.- 6.3. Degenerate symbols.- 6.4. Spline approximation methods.- XVIII. Approximate solution ot multidimensional singular integral equations.-
    1. Approximate computation of singular integrals.-
    2. An iteration method.-
    3. The Bubnov-Galerkin and the least squares methods.-
    4. Coordinate functions connected with spherical functions.-
    5. The case of exactly known eigenfunctions.-
    6. Approximate construction of the eigenfunctions.-
    7. Constructing the approximations and estimating them.-
    8. Applications to one-dimensional singular equations.-
    9. Application of Hermite functions.- References.- Symbols and notations.- Name index.