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Linear Functional Analysis

Joan Cerdà Universitat de Barcelona, Barcelona, Spain
Available Formats:
Hardcover ISBN: 978-0-8218-5115-9
Product Code: GSM/116
List Price: $70.00 MAA Member Price:$63.00
AMS Member Price: $56.00 Electronic ISBN: 978-1-4704-1178-7 Product Code: GSM/116.E List Price:$66.00
MAA Member Price: $59.40 AMS Member Price:$52.80
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $105.00 MAA Member Price:$94.50
AMS Member Price: $84.00 Click above image for expanded view Linear Functional Analysis Joan Cerdà Universitat de Barcelona, Barcelona, Spain Available Formats:  Hardcover ISBN: 978-0-8218-5115-9 Product Code: GSM/116  List Price:$70.00 MAA Member Price: $63.00 AMS Member Price:$56.00
 Electronic ISBN: 978-1-4704-1178-7 Product Code: GSM/116.E
 List Price: $66.00 MAA Member Price:$59.40 AMS Member Price: $52.80 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$105.00 MAA Member Price: $94.50 AMS Member Price:$84.00
• Book Details

Volume: 1162010; 330 pp
MSC: Primary 46; Secondary 47;

Functional analysis studies the algebraic, geometric, and topological structures of spaces and operators that underlie many classical problems. Individual functions satisfying specific equations are replaced by classes of functions and transforms that are determined by the particular problems at hand.

This book presents the basic facts of linear functional analysis as related to fundamental aspects of mathematical analysis and their applications. The exposition avoids unnecessary terminology and generality and focuses on showing how the knowledge of these structures clarifies what is essential in analytic problems.

The material in the first part of the book can be used for an introductory course on functional analysis, with an emphasis on the role of duality. The second part introduces distributions and Sobolev spaces and their applications. Convolution and the Fourier transform are shown to be useful tools for the study of partial differential equations. Fundamental solutions and Green's functions are considered and the theory is illustrated with several applications. In the last chapters, the Gelfand transform for Banach algebras is used to present the spectral theory of bounded and unbounded operators, which is then used in an introduction to the basic axioms of quantum mechanics.

The presentation is intended to be accessible to readers whose backgrounds include basic linear algebra, integration theory, and general topology. Almost 240 exercises will help the reader in better understanding the concepts employed.

This book is published in cooperation with Real Sociedád Matematica Española.

Graduate students interested in functional analysis, PDEs, analysis.

• Chapters
• Chapter 1. Introduction
• Chapter 2. Normed spaces and operators
• Chapter 3. Fréchet spaces and Banach theorems
• Chapter 4. Duality
• Chapter 5. Weak topologies
• Chapter 6. Distributions
• Chapter 7. Fourier transform and Sobolev spaces
• Chapter 8. Banach algebras
• Chapter 9. Unbounded operators in a Hilbert space
• Hints to exercises

• Reviews

• Overall, this is an interesting and well-written book, covering a lot of material. I found it very readable... The discussion is well motivated mathematically (there are few applications to other areas) and full details of proofs are given, so it is fairly self-contained.

Bryan P. Rynne, Mathematical Reviews
• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1162010; 330 pp
MSC: Primary 46; Secondary 47;

Functional analysis studies the algebraic, geometric, and topological structures of spaces and operators that underlie many classical problems. Individual functions satisfying specific equations are replaced by classes of functions and transforms that are determined by the particular problems at hand.

This book presents the basic facts of linear functional analysis as related to fundamental aspects of mathematical analysis and their applications. The exposition avoids unnecessary terminology and generality and focuses on showing how the knowledge of these structures clarifies what is essential in analytic problems.

The material in the first part of the book can be used for an introductory course on functional analysis, with an emphasis on the role of duality. The second part introduces distributions and Sobolev spaces and their applications. Convolution and the Fourier transform are shown to be useful tools for the study of partial differential equations. Fundamental solutions and Green's functions are considered and the theory is illustrated with several applications. In the last chapters, the Gelfand transform for Banach algebras is used to present the spectral theory of bounded and unbounded operators, which is then used in an introduction to the basic axioms of quantum mechanics.

The presentation is intended to be accessible to readers whose backgrounds include basic linear algebra, integration theory, and general topology. Almost 240 exercises will help the reader in better understanding the concepts employed.

This book is published in cooperation with Real Sociedád Matematica Española.

Graduate students interested in functional analysis, PDEs, analysis.

• Chapters
• Chapter 1. Introduction
• Chapter 2. Normed spaces and operators
• Chapter 3. Fréchet spaces and Banach theorems
• Chapter 4. Duality
• Chapter 5. Weak topologies
• Chapter 6. Distributions
• Chapter 7. Fourier transform and Sobolev spaces
• Chapter 8. Banach algebras
• Chapter 9. Unbounded operators in a Hilbert space
• Hints to exercises
• Overall, this is an interesting and well-written book, covering a lot of material. I found it very readable... The discussion is well motivated mathematically (there are few applications to other areas) and full details of proofs are given, so it is fairly self-contained.

Bryan P. Rynne, Mathematical Reviews
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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