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A Course in Functional Analysis and Measure Theory

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概要 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.続きを見る
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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本文を見る Full text available from Springer Mathematics and Statistics eBooks 2018 English/International

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登録日 2020.06.27
更新日 2020.06.28