**Graduate Studies in Mathematics**

Volume: 116;
2010;
330 pp;
Hardcover

MSC: Primary 46;
Secondary 47

Print ISBN: 978-0-8218-5115-9

Product Code: GSM/116

List Price: $66.00

Individual Member Price: $52.80

**Electronic ISBN: 978-1-4704-1178-7
Product Code: GSM/116.E**

List Price: $66.00

Individual Member Price: $52.80

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#### Supplemental Materials

# Linear Functional Analysis

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*Joan Cerdà*

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 Sociedad Matemática Española (RSME)

#### Readership

Graduate students interested in functional analysis, PDEs, analysis.

#### Reviews & Endorsements

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

#### Table of Contents

# Table of Contents

## Linear Functional Analysis

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface xi12 free
- Introduction 116 free
- Normed spaces and operators 2540 free
- Fréchet spaces and Banach theorems 7590
- Duality 93108
- Weak topologies 127142
- Distributions 143158
- Fourier transform and Sobolev spaces 181196
- Banach algebras 227242
- Unbounded operators in a Hilbert space 257272
- Hints to exercises 299314
- Bibliography 321336
- Index 325340 free
- Back Cover Back Cover1346