Lecture notes on functional analysis with applications to linear partial differential equations
著者
書誌事項
Lecture notes on functional analysis with applications to linear partial differential equations
（Graduate studies in mathematics, v. 143）
American Mathematical Society, c2013
- タイトル別名
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Lecture notes on functional analysis
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注記
Includes bibliographical references (p. 245-246) and index
内容説明・目次
内容説明
This textbook is addressed to graduate students in mathematics or other disciplines who wish to understand the essential concepts of functional analysis and their applications to partial differential equations. The book is intentionally concise, presenting all the fundamental concepts and results but omitting the more specialized topics. Enough of the theory of Sobolev spaces and semigroups of linear operators is included as needed to develop significant applications to elliptic, parabolic, and hyperbolic PDEs. Throughout the book, care has been taken to explain the connections between theorems in functional analysis and familiar results of finite-dimensional linear algebra. The main concepts and ideas used in the proofs are illustrated with a large number of figures. A rich collection of homework problems is included at the end of most chapters. The book is suitable as a text for a one-semester graduate course.
目次
Preface
Chapter 1. Introduction
Chapter 2. Banach spaces
Chapter 3. Spaces of continuous functions
Chapter 4. Bounded linear operators
Chapter 5. Hilbert spaces
Chapter 6. Compact operators on a Hilbert space
Chapter 7. Semigroups of linear operators
Chapter 8. Sobolev spaces
Chapter 9. Linear partial differential equations
Chapter 10. Background material
Summary of notation
Bibliography
Index
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