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Applications of functional analysis and operator theory [electronic resource].
- 作者： Hutson, V.
- 其他作者：
- 出版： Amsterdam ;Boston : Elsevier
- 版本：2nd ed. /
- 叢書名： Mathematics in science and engineeringv. 200
- 主題： Functional analysis , Operator theory , Electronic books.
- ISBN： 9780444517906 、 0444517901
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FIND@SFXID:
CGU
- 資料類型: 電子書
- 內容註: Includes bibliographical references (p. 409-416) and index. Preface. -- Acknowledgements. -- Contents. -- 1. Banach Spaces -- 1.1 Introduction -- 1.2 Vector Spaces -- 1.3 Normed Vector Spaces -- 1.4 Banach Spaces -- 1.5 Hilbert Space -- Problems -- 2. Lebesgue Integration and the Lp Spaces -- 2.1 Introduction -- 2.2 The Measure of a Set -- 2.3 Measurable Functions -- 2.4 Integration -- 2.5 The Lp Spaces -- 2.6 Applications -- Problems -- 3. Foundations of Linear Operator Theory -- 3.1 Introduction -- 3.2 The Basic Terminology of Operator Theory -- 3.3 Some Algebraic Properties of Linear Operators -- 3.4 Continuity and Boundedness -- 3.5 Some Fundamental Properties of Bounded Operators -- 3.6 First Results on the Solution of the Equation Lf=g -- 3.7 Introduction to Spectral Theory -- 3.8 Closed Operators and Differential Equations -- Problems -- 4. Introduction to Nonlinear Operators -- 4.1 Introduction -- 4.2 Preliminaries -- 4.3 The Contraction Mapping Principle -- 4.4 The Frechet Derivative -- 4.5 Newton's Method for Nonlinear Operators -- Problems -- 5. Compact Sets in Banach Spaces -- 5.1 Introduction -- 5.2 Definitions -- 5.3 Some Consequences of Compactness -- 5.4 Some Important Compact Sets of Functions -- Problems -- 6. The Adjoint Operator -- 6.1 Introduction -- 6.2 The Dual of a Banach Space -- 6.3 Weak Convergence -- 6.4 Hilbert Space -- 6.5 The Adjoint of a Bounded Linear Operator -- 6.6 Bounded Self-adjoint Operators -- Spectral Theory -- 6.7 The Adjoint of an Unbounded Linear Operator in Hilbert Space -- Problems -- 7. Linear Compact Operators -- 7.1 Introduction -- 7.2 Examples of Compact Operators -- 7.3 The Fredholm Alternative -- 7.4 The Spectrum -- 7.5 Compact Self-adjoint Operators -- 7.6 The Numerical Solution of Linear Integral Equations -- Problems -- 8. Nonlinear Compact Operators and Monotonicity -- 8.1 Introduction -- 8.2 The Schauder Fixed Point Theorem -- 8.3 Positive and Monotone Operators in Partially Ordered Banach Spaces -- Problems -- 9. The Spectral Theorem -- 9.1 Introduction -- 9.2 Prel
- 摘要註: Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations. The present book provides, by careful selection of material, a collection of concepts and techniques essential for the modern practitioner. Emphasis is placed on the solution of equations (including nonlinear and partial differential equations). The assumed background is limited to elementary real variable theory and finite-dimensional vector spaces. Key Features - Provides an ideal transition between introductory math courses and advanced graduate study in applied mathematics, the physical sciences, or engineering. - Gives the reader a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results. - Introduces each new topic with a clear, concise explanation. - Includes numerous examples linking fundamental principles with applications. - Solidifies the readers understanding with numerous end-of-chapter problems. Provides an ideal transition between introductory math courses and advanced graduate study in applied mathematics, the physical sciences, or engineering. Gives the reader a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results. Introduces each new topic with a clear, concise explanation. Includes numerous examples linking fundamental principles with applications. Solidifies the reader's understanding with numerous end-of-chapter problems.
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讀者標籤：
- 系統號： 005051478 | 機讀編目格式
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