Functional Analysis : A Terse Introduction / Humberto Rafeiro, Gerardo Chacón, Juan Camilo Vallejo.

Format:

Book

Author/Creator:

Chacón, Gerardo, author.

Rafeiro, Humberto, author.

Vallejo, Juan Camilo, author.

Series:

De Gruyter Textbook

Language:

English

Subjects (All):

Functional analysis--Textbooks.

Functional analysis.

Algebras, Linear--Textbooks.

Algebras, Linear.

Physical Description:

1 online resource (246 pages) : illustrations

Edition:

1st ed.

Place of Publication:

Berlin ; Boston : De Gruyter, [2016]

Language Note:

In English.

Summary:

This textbook on functional analysis offers a short and concise introduction to the subject. The book is designed in such a way as to provide a smooth transition between elementary and advanced topics and its modular structure allows for an easy assimilation of the content. Starting from a dedicated chapter on the axiom of choice, subsequent chapters cover Hilbert spaces, linear operators, functionals and duality, Fourier series, Fourier transform, the fixed point theorem, Baire categories, the uniform bounded principle, the open mapping theorem, the closed graph theorem, the Hahn-Banach theorem, adjoint operators, weak topologies and reflexivity, operators in Hilbert spaces, spectral theory of operators in Hilbert spaces, and compactness. Each chapter ends with workable problems.The book is suitable for graduate students, but also for advanced undergraduates, in mathematics and physics. Contents:List of FiguresBasic NotationChoice PrinciplesHilbert SpacesCompleteness, Completion and DimensionLinear OperatorsFunctionals and Dual SpacesFourier SeriesFourier TransformFixed Point TheoremBaire Category TheoremUniform Boundedness PrincipleOpen Mapping TheoremClosed Graph TheoremHahn-Banach TheoremThe Adjoint OperatorWeak Topologies and ReflexivityOperators in Hilbert SpacesSpectral Theory of Operators on Hilbert SpacesCompactnessBibliographyIndex

Contents:

Frontmatter

Contents

List of Figures

Basic Notation

1. Choice Principles

2. Hilbert Spaces

3. Completeness, Completion and Dimension

4. Linear Operators

5. Functionals and Dual Spaces

6. Fourier Series

7. Fourier Transform

8. Fixed Point Theorem

9. Baire Category Theorem

10. Uniform Boundedness Principle

11. Open Mapping Theorem

12. Closed Graph Theorem

13. Hahn-Banach Theorem

14. The Adjoint Operator

15. Weak Topologies and Reflexivity

16. Operators in Hilbert Spaces

17. Spectral Theory of Operators on Hilbert Spaces

18. Compactness

Bibliography

Index

Notes:

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 26. Mrz 2019)

ISBN:

9783110441925

3110441926

OCLC:

979882989