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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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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
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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3.

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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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
4.

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
5.

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
6.

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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7.

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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8.

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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9.

図書

図書
Л.В. Канторович и Г.П. Акилов
出版情報: Москва : Государственное изд-во физико-математической литературы, 1959  684 p ; 23 cm
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10.

図書

図書
Michael Pedersen
出版情報: Boca Raton, Fla : Chapman & Hall/CRC, c2000  298 p. ; 25 cm
シリーズ名: Studies in advanced mathematics
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目次情報: 続きを見る
Topological and Metric Spaces / 1:
Some Topology / 1.1:
Metric Spaces / 1.2:
Banach Spaces / 2:
Normed Vector Spaces / 2.1:
L[superscript p]-spaces / 2.2:
Infinite Dimensional Spaces / 2.3:
Bounded Operators / 3:
Basic Properties / 3.1:
Bounded Linear Operators / 3.2:
Hilbert Spaces / 4:
Inner Product Spaces / 4.1:
Construction of Hilbert Spaces / 4.2:
Orthogonal Projection and Complement / 4.4:
Weak Convergence / 4.5:
Operators on Hilbert Spaces / 5:
The Adjoint of a Bounded Operator / 5.1:
Compactness and Compact Operators / 5.2:
Closed Operators / 5.3:
The Adjoint of an Unbounded Operator / 5.4:
Spectral Theory / 6:
The Spectrum and the Resolvent / 6.1:
Operator-Valued Functions / 6.2:
Integral Operators / 7:
Introduction / 7.1:
The Class of Hilbert-Schmidt Operators / 7.2:
Integral Equations / 7.3:
Semigroups of Evolution / 8:
Strongly Continuous Semigroups / 8.1:
The Resolvent / 8.2:
Sobolev Spaces / 9:
Basic Definitions / 9.1:
Density Theorems / 9.2:
Extension Theorems / 9.3:
Imbedding Theorems / 9.4:
Example / 9.4.1:
Applications / 9.4.2:
The Trace Theorem / 9.4.3:
Negative Sobolev Spaces and Duality / 9.6:
Interpolation Spaces / 10:
Intermediate and Interpolation Spaces / 10.1:
The Operator L / 10.1.1:
Intermediate Derivatives Theorem / 10.2:
An Example / 10.2.1:
A Continuity Property / 10.2.2:
Interpolation Theorem / 10.3:
Reiteration Properties / 10.3.1:
Duality / 10.3.2:
Interpolation / 10.4:
Interpolation with Hilbert Range / 10.5:
The Space L[superscript p] (0, T; X) / 10.5.1:
Distributions on ]0, T[ with Values in X / 10.5.2:
Interpolation between L[superscript p] (0, T; H) Spaces / 10.5.3:
Linear Elliptic Operators / 11:
Elliptic Operators / 11.1:
The Dirichlet Problem, Types of Solutions / 11.2:
Boundary Operators / 11.3:
Elliptic Equations / 11.3.1:
The Formal Adjoint of A / 11.3.2:
A Modified Version of Green's Formula / 11.3.3:
V-elliptic and V-coercive Forms / 11.4:
The Boundary Conditions / 11.5:
Realization of the Operator A / 11.5.1:
The V-space / 11.5.2:
Variational Formulation / 11.6:
Assumptions for the Variational Problem / 11.7:
A Classical Regularity Result / 11.8:
A Regularity Theorem / 11.8.1:
An Abstract Regularity Theorem / 11.8.2:
Transposition / 11.9:
Transposition of Nonhomogeneous Boundary Value Problems / 11.9.1:
Regularity of Hyperbolic Mixed Problems / 12:
Solvability Results / 12.1:
Classical Solvability Results / 12.1.1:
Newer Solvability Theorems / 12.1.2:
A Discussion of the Regularity Results / 12.1.3:
Proofs of the Newer Regularity Theorems / 12.2:
Proofs of Theorems from 12.1.2 / 12.2.1:
Interpolation Results / 12.3:
Some Additional Regularity Theorems / 12.4:
Systems with Variable Coefficients / 12.5:
The Hilbert Uniqueness Method / 12.5.1:
Dirichlet Boundary Control / 13.1:
Application of HUM / 13.1.1:
Preliminary Lemmas / 13.1.2:
A Discussion of the Control Area / 13.1.3:
Exact Controllability in Polygons and Polyhedra / 13.1.4:
The Problem of Exact Controllability / 13.2:
The Operator A / 13.2.2:
The Variable Coefficients Case / 13.3:
Notation and Properties of the Operator A / 13.3.1:
Exercises / 13.3.2:
References
Topological and Metric Spaces / 1:
Some Topology / 1.1:
Metric Spaces / 1.2:
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