Linear Integral Equations; Applied Mathematical Sciences, 82 - gebunden oder broschiert

EAN (ISBN-13): 9780387987002
ISBN (ISBN-10): 0387987002
Gebundene Ausgabe
Erscheinungsjahr: 1999
Herausgeber: Springer-Verlag New York Inc.
388 Seiten
Gewicht: 0,742 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 2007-06-15T07:50:10+02:00 (Berlin)
Detailseite zuletzt geändert am 2024-02-27T22:07:33+01:00 (Berlin)
ISBN/EAN: 0387987002

ISBN - alternative Schreibweisen:
0-387-98700-2, 978-0-387-98700-2
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: kozlov, maz, rainer, kress, kreß
Titel des Buches: linear integral equations, intégral

---

Daten vom Verlag:

Autor/in: Rainer Kress
Titel: Applied Mathematical Sciences; Linear Integral Equations
Verlag: Springer; Springer US
367 Seiten
Erscheinungsjahr: 1999-03-26
New York; NY; US
Gewicht: 1,590 kg
Sprache: Englisch
160,49 € (DE)
164,99 € (AT)
196,69 CHF (CH)
Not available, publisher indicates OP

BB; Book; Hardcover, Softcover / Mathematik/Analysis; Mathematische Analysis, allgemein; Verstehen; minimum; functional analysis; numerical methods; compactness; calculus; Sobolev space; Integral calculus; Integral Equations; Integral equation; logarithm; Linear Integral Equations; Boundary value problem; C; Analysis; Mathematics and Statistics; BB; BB; BC; EA

1 Normed Spaces.- 1.1 Convergence and Continuity.- 1.2 Completeness.- 1.3 Compactness.- 1.4 Scalar Products.- 1.5 Best Approximation.- Problems.- 2 Bounded and Compact Operators.- 2.1 Bounded Operators.- 2.2 Integral Operators.- 2.3 Neumann Series.- 2.4 Compact Operators.- Problems.- 3 Riesz Theory.- 3.1 Riesz Theory for Compact Operators.- 3.2 Spectral Theory for Compact Operators.- 3.3 Volterra Integral Equations.- Problems.- 4 Dual Systems and Fredholm Alternative.- 4.1 Dual Systems via Bilinear Forms.- 4.2 Dual Systems via Sesquilinear Forms.- 4.3 The Fredholm Alternative.- 4.4 Boundary Value Problems.- Problems.- 5 Regularization in Dual Systems.- 5.1 Regularizers.- 5.2 Normal Solvability.- 5.3 Index.- Problems.- 6 Potential Theory.- 6.1 Harmonic Functions.- 6.2 Boundary Value Problems: Uniqueness.- 6.3 Surface Potentials.- 6.4 Boundary Value Problems: Existence.- 6.5 Nonsmooth Boundaries.- Problems.- 7 Singular Integral Equations.- 7.1 Hölder Continuity.- 7.2 The Cauchy Integral Operator.- 7.3 The Riemann Problem.- 7.4 Integral Equations with Cauchy Kernel.- 7.5 Cauchy Integral and Logarithmic Potential.- 7.6 Logarithmic Single-Layer Potential on an Arc.- Problems.- 8 Sobolev Spaces.- 8.1 The Sobolev Space Hp[0, 2?].- 8.2 The Sobolev Space Hp(?).- 8.3 Weak Solutions to Boundary Value Problems.- Problems.- 9 The Heat Equation.- 9.1 Initial Boundary Value Problem: Uniqueness.- 9.2 Heat Potentials.- 9.3 Initial Boundary Value Problem: Existence.- Problems.- 10 Operator Approximations.- 10.1 Approximations via Norm Convergence.- 10.2 Uniform Boundedness Principle.- 10.3 Collectively Compact Operators.- 10.4 Approximations via Pointwise Convergence.- 10.5 Successive Approximations.- Problems.- 11 Degenerate Kernel Approximation.- 11.1 Degenerate Operators and Kernels.- 11.2 Interpolation.- 11.3 Trigonometric Interpolation.- 11.4 Degenerate Kernels via Interpolation.- 11.5 Degenerate Kernels via Expansions.- Problems.- 12 Quadrature Methods.- 12.1 Numerical Integration.- 12.2 Nyström’s Method.- 12.3 Weakly Singular Kernels.- 12.4 Nyström’s Method in Sobolev Spaces.- Problems.- 13 Projection Methods.- 13.1 The Projection Method.- 13.2 Projection Methods for Equations of the Second Kind.- 13.3 The Collocation Method.- 13.4 Collocation Methods for Equations of the First Kind.- 13.5 The Galerkin Method.- Problems.- 14 Iterative Solution and Stability.- 14.1 Stability of Linear Systems.- 14.2 Two-Grid Methods.- 14.3 Multigrid Methods.- 14.4 Fast Matrix-Vector Multiplication.- Problems.- 15 Equations of the First Kind.- 15.1 Ill-Posed Problems.- 15.2 Regularization of 1ll-Posed Problems.- 15.3 Compact Self-Adjoint Operators.- 15.4 Singular Value Decomposition.- 15.5 Regularization Schemes.- Problems.- 16 Tikhonov Regularization.- 16.1 The Tikhonov Functional.- 16.2 Weak Convergence.- 16.3 Quasi-Solutions.- 16.4 Minimum Norm Solutions.- 16.5 Classical Tikhonov Regularization.- Problems.- 17 Regularization by Discretization.- 17.1 Projection Methods for Ill-Posed Equations.- 17.2 The Moment Method.- 17.3 Hilbert Spaces with Reproducing Kernel.- 17.4 Moment Collocation.- Problems.- 18 Inverse Boundary Value Problems.- 18.1 Ill-Posed Equations in Potential Theory.- 18.2 An Inverse Problem in Potential Theory.- 18.3 Approximate Solution via Potentials.- 18.4 Differentiability with Respect to the Boundary.- Problems.- References.
This book resulted from the author's fascination with the mathematical beauty of integral equations. It is an attempt to combine theory, applications, and numerical methods, and cover each of these fields with the same weight. In order to make the book accessible to mathematicians, physicists, and engineers, the author has made the work as self-contained as possible, by requiring only a solid foundation in differential integral calculus. The functional analysis which is necessary for an adequate treatment of the theory and the numerical solution of integral equations is developed within the book. Problems are included at the end of each chapter.