现代数学物理方法 第1卷（影印版）
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- 原书名：Methods of Modern Mathematical Physics I
- 原出版社： Elsevier(Singapore)
- 作者： M.Reed,B.Simon
- 出版社：世界图书出版公司
- ISBN：7506259311
- 上架时间：2004-9-30
- 出版日期：2003 年6月
- 开本：24开
- 页码：400
- 版次：1-1
- 所属分类：
数学 > 文科、经管、金融、工程数学 > 数学交叉学科
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内容简介回到顶部↑
This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modem mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modem physics, and partial differenrial equations.
目录回到顶部↑
preface
introduction
contents of other volumes
i: preliminaries
1. sets and functions
2. metric and normed linear spaces
appendix lira sup and lim inf
3. the lebesgue integral
4. abstract measure theory
5. two conrergence arguments
6. equicontinuity
notes
problems
ii: hilbert spaces
1. the geometry of hilbert space
2. the riesz lemma
3. orthonormal bases
4. tensor products of hilbert spaces
5. ergodic theory: an introduction
notes
introduction
contents of other volumes
i: preliminaries
1. sets and functions
2. metric and normed linear spaces
appendix lira sup and lim inf
3. the lebesgue integral
4. abstract measure theory
5. two conrergence arguments
6. equicontinuity
notes
problems
ii: hilbert spaces
1. the geometry of hilbert space
2. the riesz lemma
3. orthonormal bases
4. tensor products of hilbert spaces
5. ergodic theory: an introduction
notes
前言回到顶部↑
This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modem mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modem physics, and partial differenrial equations.
This revised and enlarged edition differs from the first in two major ways. First, many colleagues have suggested to us that it would be helpful to include some material on the Fourier transform in Volume I so that this important topic can be conveniently included in a standard functional analysis course using this book. Thus, we have included in this edition Sections IX. 1, IX.2, and part of IX.3 from Volume II and some additional material, together with relevant notes and problems. Secondly, we have included a variety of supplementary material at the end of the book. Some of these supplementary sections provide proofs of theorems in Chapters II-IV which were omitted in the first edition. While these proofs make Chapters II-IV more self-contained, we still recommend that students with no previous experience with this material consult more elementary texts. Other supplementary sections provide expository material to aid the instructor and the .student (for example, "Applications of Compact Operators"). Still other sections introduce and develop new material (for example, "Minimization of Functionals").
It gives us pleasure to thank many individuals:
The students who took our course in 1970- 1971 and especially J. E. Taylor for constructive comments about the lectures and lecture notes.
L. Gross, T. Kato, and especially D. Ruelle for reading parts of the manuscript and for making numerous suggestions and corrections.
F. Armstrong, E. Epstein, B. Farrell, and H. Wertz for excellent typing.
M. Goldberger, E. Nelson, M. Simon, E. Stein, and A. Wightman for aid and encouragement.
MIKE REED
BARRY SIMON
April 1980
This revised and enlarged edition differs from the first in two major ways. First, many colleagues have suggested to us that it would be helpful to include some material on the Fourier transform in Volume I so that this important topic can be conveniently included in a standard functional analysis course using this book. Thus, we have included in this edition Sections IX. 1, IX.2, and part of IX.3 from Volume II and some additional material, together with relevant notes and problems. Secondly, we have included a variety of supplementary material at the end of the book. Some of these supplementary sections provide proofs of theorems in Chapters II-IV which were omitted in the first edition. While these proofs make Chapters II-IV more self-contained, we still recommend that students with no previous experience with this material consult more elementary texts. Other supplementary sections provide expository material to aid the instructor and the .student (for example, "Applications of Compact Operators"). Still other sections introduce and develop new material (for example, "Minimization of Functionals").
It gives us pleasure to thank many individuals:
The students who took our course in 1970- 1971 and especially J. E. Taylor for constructive comments about the lectures and lecture notes.
L. Gross, T. Kato, and especially D. Ruelle for reading parts of the manuscript and for making numerous suggestions and corrections.
F. Armstrong, E. Epstein, B. Farrell, and H. Wertz for excellent typing.
M. Goldberger, E. Nelson, M. Simon, E. Stein, and A. Wightman for aid and encouragement.
MIKE REED
BARRY SIMON
April 1980
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