Functional Analysis

Gerardo Chacón, Humberto Rafeiro, Juan Camilo Vallejo

ISBN 10: 3110441918 / ISBN 13: 9783110441918

Published by De Gruyter, DE, 2016

About this Item

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.

Seller Inventory # LU-9783110441918

Bibliographic Details

• Title: Functional Analysis
• Publisher: De Gruyter, DE
• Publication Date: 2016
• Language: English
• ISBN 10: 3110441918
• ISBN 13: 9783110441918
• Binding: Paperback
• Condition: New
• Weight: 477 grams

About this title

Synopsis

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 Figures
Basic Notation
Choice Principles
Hilbert Spaces
Completeness, Completion and Dimension
Linear Operators
Functionals and Dual Spaces
Fourier Series
Fourier Transform
Fixed Point Theorem
Baire Category Theorem
Uniform Boundedness Principle
Open Mapping Theorem
Closed Graph Theorem
Hahn–Banach Theorem
The Adjoint Operator
Weak Topologies and Reflexivity
Operators in Hilbert Spaces
Spectral Theory of Operators on Hilbert Spaces
Compactness
Bibliography
Index

About the Author

Gerardo Chacón, Gallaudet University, DC, USA.
Humberto Rafeiro, Juan Vallejo, Pontificia Universidad Javeriana, Bogota, Colombia.