Elements of functional analysis

著者

• Maddox, I. J. (Ivor John)

書誌事項

Elements of functional analysis

I.J. Maddox

Cambridge University Press, 1988

2nd ed.

• : pbk.

注記

Bibliography: p. 238

Includes index

内容説明・目次

内容説明

The second edition of this successful textbook, first published in 1970, retains the aims of the first, namely to provide a truly introductory course in functional analysis, but the opportunity has been taken to add more detail and worked examples. The main changes are complete revisons of the work on convex sets, metric and topological linear spaces, reflexivity and weak convergence. Additional material on the Weiner algebra of absolutely convergent Fourier series and on weak topologies is included. A final chapter includes elementary applications of functional analysis to differential and integral equations.

目次

• Preface to the second edition
• Preface to the first edition
• Part I. Basic Set Theory and Analysis: 1. Sets and functions
• 2. Real and complex numbers
• 3. Sequences of functions, continuity, differentiability
• 4. Inequalities
• Part II. Metric and Topological Spaces: 1. Metric and semimetric spaces
• 2. Complete metric spaces
• 3. Some metric and topological concepts
• 4. Continuous functions on metric and topological spaces
• 5. Compact sets
• 6. Category and uniform boundedness
• Part III. Linear and Linear Metric Spaces: 1. Linear spaces
• 2. Subspaces, dimensionality, factorspaces, convex sets
• 3. Metric linear spaces, topological linear spaces
• 4. Basis
• Part IV. Normed Linear Spaces: 1. Convergence and completeness
• 2. Linear operators and functionals
• 3. The Banach-Steinhaus theorem
• 4. The open mapping and closed graph theorems
• 5. The Hahn-Banach extension
• 6. Weak topology and weak convergence
• Part V. 1. Algebras and Banach algebras
• 2. Homomorphisms and isomorphisms
• 3. The spectrum and the Gelfand-Mazaur theorem
• 4. The Weiner algebra
• Part VI. Hilbert Space: 1. Inner product and Hilbert spaces
• 2. Orthonormal sets
• 3. The dual space of a Hilbert space
• 4. Symmetric and compact operators
• Part VII. Applications: 1. Differential and integral problems
• 2. The Sturm-Liouville problem
• 3. Matrix transformations in sequence spaces
• Appendix
• Bibliography
• Index.

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詳細情報

• NII書誌ID(NCID): BA05081160
• ISBN:
  • 0521353505
  • 052135868X
• LCCN: 88022891
• 出版国コード: uk
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Cambridge [Cambridgeshire] ; New York
• ページ数/冊数: xii, 242 p.
• 大きさ: 23 cm
• 分類:
  • LCC : QA320
  • DC19 : 515.7
• 件名:
  • LCSH : Functional analysis