Elements of the Theory of Functions and Functional Analysis

Elements of the Theory of Functions and Functional Analysis
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作者: ,
1999-02
版次: 1
ISBN: 9780486406831
定价: 147.50
装帧: 平装
开本: 其他
纸张: 胶版纸
页数: 288页
正文语种: 英语
  • Basedontheauthors'coursesandlectures,thistwo-partadvanced-leveltextisnowavailableinasinglevolume.Topicsincludemetricandnormedspaces,continuouscurvesinmetricspaces,measuretheory,Lebesqueintervals,Hilbertspace,andmore.Eachsectioncontainsexercises.Listsofsymbols,definitions,andtheorems.1957edition. Preface

    Translator's Note

    CHAPTER I

    FUNDAMENTALS OF SET THEORY

       1. The Concept of Set. Operations on Sets

      2. Finite and Infinite Sets. Denumerability

      3. Equivalence of Sets

      4. The Nondenumerability of the Set of Real Numbers

      5. The Concept of Cardinal Number

      6. Partition into Classes

      7. Mappings of Sets. General Concept of Function

    CHAPTER II

    METRIC SPACES

      8. Definition and Examples of Metric Spaces

      9. Convergence of Sequences. Limit Points

      10. Open and Closed Sets

      11. Open and Closed Sets on the Real Line

      12. Continuous Mappings. Homeomorphism. Isometry

      13. Complete Metric Spaces 

      14. The Principle of Contraction Mappings and its Applications

      15. Applications of the Principle of Contraction Mappings in Analysis

      16. Compact Sets in Metric Spaces

      17. Arzela.'s Theorem and its Applications

      18. Compacts

      19. Real Functions in Metric Spaces

      20. Continuous Curves in Metric Spaces

    CHAPTER III

    NORMED LINEAR SPACES

      21. Definition and Examples of Normed Linear Spaces

      22. Convex Sets in Normed Linear Spaces

      23. Linear Functionals

      24. The Conjugate Space

      25. Extension of Linear Functionals

      26. The Second Conjugate Space

      27. Weak Convergence

      28. Weak Convergence of Linear Functionals

      29. Linear Operators

    ADDENDUM TO CHAPTER IIl

    GENERALIZED FUNCTIONS

    CHAPTER IV

    LINEAR OPERATOR EQUATIONS

      30. Spectrum of an Operator. Resolvents

      31. Completely Continuous Operators

      32. Linear Operator Equations. Fredholm's Theorems

    LIST OF SYMBOLS

    LIST OF DEFINITIONS

    LIST OF THEOREMS

    BASIC LITERATURE

    INDEX
  • 内容简介:
    Basedontheauthors'coursesandlectures,thistwo-partadvanced-leveltextisnowavailableinasinglevolume.Topicsincludemetricandnormedspaces,continuouscurvesinmetricspaces,measuretheory,Lebesqueintervals,Hilbertspace,andmore.Eachsectioncontainsexercises.Listsofsymbols,definitions,andtheorems.1957edition.
  • 目录:
    Preface

    Translator's Note

    CHAPTER I

    FUNDAMENTALS OF SET THEORY

       1. The Concept of Set. Operations on Sets

      2. Finite and Infinite Sets. Denumerability

      3. Equivalence of Sets

      4. The Nondenumerability of the Set of Real Numbers

      5. The Concept of Cardinal Number

      6. Partition into Classes

      7. Mappings of Sets. General Concept of Function

    CHAPTER II

    METRIC SPACES

      8. Definition and Examples of Metric Spaces

      9. Convergence of Sequences. Limit Points

      10. Open and Closed Sets

      11. Open and Closed Sets on the Real Line

      12. Continuous Mappings. Homeomorphism. Isometry

      13. Complete Metric Spaces 

      14. The Principle of Contraction Mappings and its Applications

      15. Applications of the Principle of Contraction Mappings in Analysis

      16. Compact Sets in Metric Spaces

      17. Arzela.'s Theorem and its Applications

      18. Compacts

      19. Real Functions in Metric Spaces

      20. Continuous Curves in Metric Spaces

    CHAPTER III

    NORMED LINEAR SPACES

      21. Definition and Examples of Normed Linear Spaces

      22. Convex Sets in Normed Linear Spaces

      23. Linear Functionals

      24. The Conjugate Space

      25. Extension of Linear Functionals

      26. The Second Conjugate Space

      27. Weak Convergence

      28. Weak Convergence of Linear Functionals

      29. Linear Operators

    ADDENDUM TO CHAPTER IIl

    GENERALIZED FUNCTIONS

    CHAPTER IV

    LINEAR OPERATOR EQUATIONS

      30. Spectrum of an Operator. Resolvents

      31. Completely Continuous Operators

      32. Linear Operator Equations. Fredholm's Theorems

    LIST OF SYMBOLS

    LIST OF DEFINITIONS

    LIST OF THEOREMS

    BASIC LITERATURE

    INDEX
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