A course in functional analysis and measure theory

書誌事項

A course in functional analysis and measure theory

Vladimir Kadets ; translated from the Russian by Andrei Iacob

(Universitext)

Springer, c2018

タイトル別名

Курс функционального анализа

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注記

Translation of: Курс функционального анализа

Includes bibliographical references (p. 525-528) and index

内容説明・目次

内容説明

Written by an expert on the topic and experienced lecturer, this textbook provides an elegant, self-contained introduction to functional analysis, including several advanced topics and applications to harmonic analysis. Starting from basic topics before proceeding to more advanced material, the book covers measure and integration theory, classical Banach and Hilbert space theory, spectral theory for bounded operators, fixed point theory, Schauder bases, the Riesz-Thorin interpolation theorem for operators, as well as topics in duality and convexity theory. Aimed at advanced undergraduate and graduate students, this book is suitable for both introductory and more advanced courses in functional analysis. Including over 1500 exercises of varying difficulty and various motivational and historical remarks, the book can be used for self-study and alongside lecture courses.

目次

Introduction.- Chapter 1. Metric and topological spaces.- Chapter 2. Measure theory.- Chapter 3. Measurable functions.- Chapter 4. The Lebesgue integral.- Chapter 5. Linear spaces, linear functionals, and the Hahn-Banach theorem.- Chapter 6. Normed spaces.- Chapter 7. Absolute continuity of measures and functions. Connection between derivative and integral.- Chapter 8. The integral on C(K).- Chapter 9. Continuous linear functionals.- Chapter 10. Classical theorems on continuous operators.- Chapter 11. Elements of spectral theory of operators. Compact operators.- Chapter 12. Hilbert spaces.- Chapter 13. Functions of an operator.- Chapter 14. Operators in Lp.- Chapter 15. Fixed-point theorems and applications.- Chapter 16. Topological vector spaces.- Chapter 17. Elements of duality theory.- Chapter 18. The Krein-Milman theorem and applications.- References. Index.

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詳細情報

  • NII書誌ID(NCID)
    BB26563189
  • ISBN
    • 9783319920030
  • LCCN
    2018943248
  • 出版国コード
    sz
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 原本言語コード
    rus
  • 出版地
    Cham
  • ページ数/冊数
    xxii, 539 p.
  • 大きさ
    24 cm
  • 件名
  • 親書誌ID
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