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出版社:世界圖書出版公司
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ISBN:9787510096778
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作者:(美)布勒齊
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頁數:599
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出版日期:2015-07-01
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印刷日期:2015-07-01
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包裝:平裝
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開本:24開
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版次:1
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印次:1
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字數:500千字
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布勒齊著的《泛函分析索伯列夫空間和偏微分方程(英文版)》提出了一個連貫的、確切的、統一的方法將兩個來自不同領域的元素——泛函分析和偏微分方程,結合在一起,旨在為具有良好實分析背景的學生提供幫助。通過詳細地分析一維PDEs的簡單案例,即ODEs,一個對初學者來說比較簡單的方法,該書展示了從泛函分析到偏微分方程的平滑過渡。
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Preface The Hahn-Banach Theorems. Introduction to the Theory of Conjugate Convex Functions 1.1 The Analytic Form of the Hahn-Banach Theorem: Extension of Linear Functionals 1.2 The Geometric Forms of the Hahn-Banach Theorem: Separation of Convex Sets 1.3 The Bidual E. Orthogonality Relations 1.4 A Quick Introduction to the Theory of Conjugate Convex Functions Comments on Chapter 1 Exercises for Chapter 1 2 The Uniform Boundedness Principle and the Closed Graph Theorem 2.1 The Baire Category Theorem 2.2 The Uniform Boundedness Principle 2.3 The Open Mapping Theorem and the Closed Graph Theorem 2.4 Complementary Subspaces. Right and Left inve.rtibility of Linear Operators 2.5 Orthogonality Revisited 2.6 An Introduction to Unbounded Linear Operators. Definition of the Adjoint 2.7 A Characterization of Operators with Closed Range. A Characterization of Surjective Operators Comments on Chapter 2 Exercises for Chapter 2 Weak Topologies. Reflexive Spaces. Separable Spaces. Uniform Convexity 3.1 The Coarsest Topology for Which a Collection of Maps Becomes Continuous 3.2 Definition and Elementary Properties of the Weak Topology a(E, E*) 3.3 Weak Topology, Convex Sets, and Linear Operators 3.4- The Weak* Topology tr (E', E) 3.5 Reflexive Spaces 3.6 Separable Spaces 3.7 Uniformly Convex Spaces Comments on Chapter 3 Exercises for Chapter 3 4 Lp Spaces 4.1 Some Results about Integration That Everyone Must Know 4.2 Definition and Elementary Properties of Lp Spaces 4.3 Reflexivity. Separability. Dual of Lp 4.4 Convolution and regularization 4.5 Criterion for Strong Compactness in Lp Comments on Chapter 4 Exercises for Chapter 4 5 Hilbert Spaces 5.1 Definitions and Elementary Properties. Projection onto a Closed Convex Set 5.2 The Dual Space of a Hilbert Space 5.3 The Theorems of Stampacchia and Lax-Milgram 5.4 Hilbert Sums. Orthonormal Bases Comments on Chapter 5 Exercises for Chapter 5 Compact Operators. Spectral Decomposition of Self-Adjoint Compact Operators 6.1 Definitions. Elementary Properties. Adjoint 6.2 The Riesz-Fredholm Theory 6.3 The Spectrum of a Compact Operator 6.4 Spectral Decomposition of Self-Adjoint Compact Operators Comments on Chapter 6 Exercises for Chapter 6 The Hille--Yosida Theorem 7.1 Definition and Elementary Properties of Maximal Monotone Operators 7.2 Solution of the Evolution Problem du "37 + Au = 0 on [0, +cx), u(0) = u0. Existence and uniqueness 7.3 Regularity 7.4 The Self-Adjoint Case Comments on Chapter 7 8 Sobolev Spaces and the Variational Formulation of Boundary Value Problems in One Dimension 8.1 Motivation 8.2 The Sobolev Space Wl'P(l) 8.3 The Space W 'p 8.4 Some Examples of Boundary Value Problems 8.5 The Maximum Principle 8.6 Eigenfunctions and Spectral Decomposition Comments on Chapter 8 Exercises for Chapter 8 9 Sobolev Spaces and the Variational Formulation of Elliptic Boundary Value Problems in N Dimensions 9.1 Definition and Elementary Properties of the Sobolev Spaces WI,P() 9.2 Extension Operators 9.3 Sobolev Inequalities 9.4 The Space W'P(f2) 9.5 Variational Formulation of Some Boundary Value Problems 9.6 Regularity of Weak Solutions 9.7 The Maximum Principle 9.8 Eigenfunctions and Spectral Decomposition Comments on Chapter 9 . 10 Evolution Problems: The Heat Equation and the Wave Equation .. I0.1 The Heat Equation: Existence, Uniqueness, and Regularity 10.2 The Maximum Principle 10.3 The Wave Equation Comments on Chapter 10 11 Miscellaneous Complements 11.1 Finite-Dimensional and Finite-Codimensional Spaces 11.2 Quotient Spaces 11.3 Some Classical Spaces of Sequences 11.4 Banach Spaces over C: What Is Similar and What Is Different?.. Solutions of Some Exercises Problems Partial Solutions of the Problems Notation References Index
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