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Functional analysis

Author: Theo Bühler; D Salamon
Publisher: Providence, Rhode Island : American Mathematical Society, [2018]
Series: Graduate studies in mathematics, v. 191.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Functional analysis is a central subject of mathematics with applications in many areas of geometry, analysis, and physics. This book provides a comprehensive introduction to the field for graduate students and researchers. It begins in Chapter 1 with an introduction to the necessary foundations, including the Arzelà-Ascoli theorem, elementary Hilbert space theory, and the Baire Category Theorem. Chapter 2 develops  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
(DLC) 2017057159
(OCoLC)1019844666
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Theo Bühler; D Salamon
ISBN: 9781470447762 1470447762
OCLC Number: 1050364122
Description: 1 online resource.
Contents: Cover; Title page; Contents; Preface; Introduction; Chapter 1. Foundations; 1.1. Metric Spaces and Compact Sets; 1.2. Finite-Dimensional Banach Spaces; 1.3. The Dual Space; 1.4. Hilbert Spaces; 1.5. Banach Algebras; 1.6. The Baire Category Theorem; 1.7. Problems; Chapter 2. Principles of Functional Analysis; 2.1. Uniform Boundedness; 2.2. Open Mappings and Closed Graphs; 2.3. Hahn-Banach and Convexity; 2.4. Reflexive Banach Spaces; 2.5. Problems; Chapter 3. The Weak and Weak* Topologies; 3.1. Topological Vector Spaces; 3.2. The Banach-Alaoglu Theorem; 3.3. The Banach-Dieudonné Theorem 3.4. The Eberlein-Šmulyan Theorem3.5. The Kreĭn-Milman Theorem; 3.6. Ergodic Theory; 3.7. Problems; Chapter 4. Fredholm Theory; 4.1. The Dual Operator; 4.2. Compact Operators; 4.3. Fredholm Operators; 4.4. Composition and Stability; 4.5. Problems; Chapter 5. Spectral Theory; 5.1. Complex Banach Spaces; 5.2. Spectrum; 5.3. Operators on Hilbert Spaces; 5.4. Functional Calculus for Self-Adjoint Operators; 5.5. Gelfand Spectrum and Normal Operators; 5.6. Spectral Measures; 5.7. Cyclic Vectors; 5.8. Problems; Chapter 6. Unbounded Operators; 6.1. Unbounded Operators on Banach Spaces 6.2. The Dual of an Unbounded Operator6.3. Unbounded Operators on Hilbert Spaces; 6.4. Functional Calculus and Spectral Measures; 6.5. Problems; Chapter 7. Semigroups of Operators; 7.1. Strongly Continuous Semigroups; 7.2. The Hille-Yosida-Phillips Theorem; 7.3. The Dual Semigroup; 7.4. Analytic Semigroups; 7.5. Banach Space Valued Measurable Functions; 7.6. Inhomogeneous Equations; 7.7. Problems; Appendix A. Zorn and Tychonoff; A.1. The Lemma of Zorn; A.2. Tychonoff's Theorem; Bibliography; Notation; Index; Back Cover Introduction --
Foundations --
Principles of functional analysis --
The weak and weak* topologies --
Fredholm theory --
Spectral theory --
Unbounded operators --
Semigroups of operators.
Series Title: Graduate studies in mathematics, v. 191.
Responsibility: Theo Bühler, Dietmar A. Salamon.

Abstract:

Functional analysis is a central subject of mathematics with applications in many areas of geometry, analysis, and physics. This book provides a comprehensive introduction to the field for graduate  Read more...

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