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1.

図書

図書
Veli-Matti Hokkanen, Gheorghe Moroșanu
出版情報: Boca Raton, Fla. : Chapman & Hall/CRC, c2002  xiii, 243 p. ; 24 cm
シリーズ名: Research notes in mathematics ; 432
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目次情報: 続きを見る
Introduction
Preliminaries / 1:
Function and distribution spaces / 1.1:
Monotone operators, convex functions, and subdifferentials / 1.2:
Some elements of spectral theory / 1.3:
Linear evolution equations and semigroups / 1.4:
Nonlinear evolution equations / 1.5:
Elliptic boundary value problems / 2:
Nondegenerate elliptic boundary value problems / 2.1:
Degenerate elliptic boundary value problems / 2.2:
Parabolic problems with algebraic boundary conditions / 3:
Homogeneous boundary conditions / 3.1:
Nonhomogeneous boundary conditions / 3.2:
Higher regularity of solutions / 3.3:
Parabolic problems with algebraic-differential boundary conditions / 4:
Homogeneous algebraic boundary conditions / 4.1:
Nonhomogeneous algebraic boundary condition / 4.2:
Hyperbolic problems with algebraic boundary conditions / 4.3:
Existence, uniqueness, and long-time behavior of solutions / 5.1:
Hyperbolic problems with algebraic-differential boundary conditions / 5.2:
The Fourier method for abstract differential equations / 6.1:
First order linear equations / 7.1:
Semilinear first order equations / 7.2:
Second order linear equations / 7.3:
Semilinear second order equations / 7.4:
The semigroup approach for abstract differential equations / 8:
Hyperbolic partial differential systems with nonlinear boundary conditions / 8.1:
Nonlinear nonautonomous abstract differential equations / 9:
First order differential and functional equations containing subdifferentials / 9.1:
An application / 9.2:
Implicit nonlinear differential equations / 10:
Existence of solution / 10.1:
Uniqueness of solution / 10.2:
Continuous dependence of solution / 10.3:
Existence of periodic solutions / 10.4:
Index
Introduction
Preliminaries / 1:
Function and distribution spaces / 1.1:
2.

図書

図書
by L.P. Lebedev, I.I. Vorovich and G.M.L. Gladwell
出版情報: Dordrecht : Kluwer Academic, c2002  x, 247 p. ; 25 cm
シリーズ名: Solid mechanics and its applications ; v. 100
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目次情報: 続きを見る
Introduction / 1:
Real and complex numbers / 1.1:
Theory of functions / 1.2:
Weierstrass' polynomial approximation theorem / 1.3:
Introduction to Metric Spaces / 2:
Preliminaries / 2.1:
Sets in a metric space / 2.2:
Some metric spaces of functions / 2.3:
Convergence in a metric space / 2.4:
Complete metric spaces / 2.5:
The completion theorem / 2.6:
An introduction to operators / 2.7:
Normed linear spaces / 2.8:
An introduction to linear operators / 2.9:
Some inequalities / 2.10:
Lebesgue spaces / 2.11:
Inner product spaces / 2.12:
Energy Spaces and Generalized Solutions / 3:
The rod / 3.1:
The Euler-Bernoulli beam / 3.2:
The membrane / 3.3:
The plate in bending / 3.4:
Linear elasticity / 3.5:
Sobolev spaces / 3.6:
Some imbedding theorems / 3.7:
Approximation in a Normed Linear Space / 4:
Separable spaces / 4.1:
Theory of approximation in a normed linear space / 4.2:
Riesz's representation theorem / 4.3:
Existence of energy solutions of some mechanics problems / 4.4:
Bases and complete systems / 4.5:
Weak convergence in a Hilbert space / 4.6:
Introduction to the concept of a compact set / 4.7:
Ritz approximation in a Hilbert space / 4.8:
Generalized solutions of evolution problems / 4.9:
Elements of the Theory of Linear Operators / 5:
Spaces of linear operators / 5.1:
The Banach-Steinhaus theorem / 5.2:
The inverse operator / 5.3:
Closed operators / 5.4:
The adjoint operator / 5.5:
Examples of adjoint operators / 5.6:
Compactness and Its Consequences / 6:
Sequentially compact [identical with] compact / 6.1:
Criteria for compactness / 6.2:
The Arzela-Ascoli theorem / 6.3:
Applications of the Arzela-Ascoli theorem / 6.4:
Compact linear operators in normed linear spaces / 6.5:
Compact linear operators between Hilbert spaces / 6.6:
Spectral Theory of Linear Operators / 7:
The spectrum of a linear operator / 7.1:
The resolvent set of a closed linear operator / 7.2:
The spectrum of a compact linear operator in a Hilbert space / 7.3:
The analytic nature of the resolvent of a compact linear operator / 7.4:
Self-adjoint operators in a Hilbert space / 7.5:
Applications to Inverse Problems / 8:
Well-posed and ill-posed problems / 8.1:
The operator equation / 8.2:
Singular value decomposition / 8.3:
Regularization / 8.4:
Morozov's discrepancy principle / 8.5:
Index
Introduction / 1:
Real and complex numbers / 1.1:
Theory of functions / 1.2:
3.

図書

図書
Peter D. Lax
出版情報: New York : John Wiley, c2002  xix, 580 p. ; 25 cm
シリーズ名: Pure and applied mathematics
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4.

図書

図書
Martin Schechter
出版情報: Providence, R.I. : American Mathematical Society, c2002  xxi, 425 p. ; 26 cm
シリーズ名: Graduate studies in mathematics ; v. 36
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目次情報: 続きを見る
Basic notions Duality Linear operators
The Riesz theory for compact operators
Fredholm operators Spectral theory
Unbounded operators Reflexive Banach spaces
Banach algebras Semigroups
Hilbert space Bilinear forms Selfadjoint operators
Measures of operators Examples and applications
Glossary Major Theorems
Bibliography
Index
Basic notions Duality Linear operators
The Riesz theory for compact operators
Fredholm operators Spectral theory
5.

図書

図書
Karen Saxe
出版情報: New York : Springer, c2002  xi, 197 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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Metric Spaces, Normed Spaces, Inner Product Spaces
The Topology of Metric Spaces
Measure and Integration
Fourier Analysis in Hilbert Space
An Introduction to Abstract Linear Operator Theory
Further Topics
Complex Numbers / Appendix A:
Basic Set Theory / Appendix B:
Metric Spaces, Normed Spaces, Inner Product Spaces
The Topology of Metric Spaces
Measure and Integration
6.

図書

図書
Kendall Atkinson, Weimin Han
出版情報: New York : Springer, c2001  xvi, 450 p. ; 24 cm
シリーズ名: Texts in applied mathematics ; 39
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Preface to the Second Edition
Preface to the First Edition
Linear Spaces
Linear Operators on Normed Spaces
Approximation Theory
Fourier Analysis and Wavelets
Nonlinear Equations and Their Solution by Iteration
Finite Difference Method
Sobolev Spaces
Variational Formulations of Elliptic Boundary Value Problems
The Galerkin Method and Its Variants
Finite Element Analysis
Elliptic Variational Inequalities and Their Numerical Approximations
Numerical Solution of Fredholm Integral Equations of the Second Kind
Boundary Integral Equations
References
Index
Preface to the Second Edition
Preface to the First Edition
Linear Spaces
7.

図書

図書
Robert R. Phelps
出版情報: Berlin ; New York : Springer-Verlag, c2001  124 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1757
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8.

図書

図書
И.М. Гразман, Ю.И. Любич
出版情報: Москва : "Наука", 1969  475 p ; 21 cm
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9.

図書

図書
R.D. Milne
出版情報: Boston ; London : Pitman Advanced Pub. Program, 1980  xv, 501 p. ; 24 cm
シリーズ名: Applicable mathematics series
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10.

図書

図書
Elias M. Stein & Rami Shakarchi
出版情報: Princeton, N.J. ; Oxford : Princeton University Press, c2005  xix, 402 p ; 24 cm
シリーズ名: Princeton lectures in analysis ; 3
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