Hardcover ISBN: | 978-0-88385-357-3 |
Product Code: | DOL/49 |
List Price: | $65.00 |
MAA Member Price: | $48.75 |
AMS Member Price: | $48.75 |
eBook ISBN: | 978-1-61444-213-4 |
Product Code: | DOL/49.E |
List Price: | $60.00 |
MAA Member Price: | $45.00 |
AMS Member Price: | $45.00 |
Hardcover ISBN: | 978-0-88385-357-3 |
eBook: ISBN: | 978-1-61444-213-4 |
Product Code: | DOL/49.B |
List Price: | $125.00 $95.00 |
MAA Member Price: | $93.75 $71.25 |
AMS Member Price: | $93.75 $71.25 |
Hardcover ISBN: | 978-0-88385-357-3 |
Product Code: | DOL/49 |
List Price: | $65.00 |
MAA Member Price: | $48.75 |
AMS Member Price: | $48.75 |
eBook ISBN: | 978-1-61444-213-4 |
Product Code: | DOL/49.E |
List Price: | $60.00 |
MAA Member Price: | $45.00 |
AMS Member Price: | $45.00 |
Hardcover ISBN: | 978-0-88385-357-3 |
eBook ISBN: | 978-1-61444-213-4 |
Product Code: | DOL/49.B |
List Price: | $125.00 $95.00 |
MAA Member Price: | $93.75 $71.25 |
AMS Member Price: | $93.75 $71.25 |
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Book DetailsDolciani Mathematical ExpositionsVolume: 49; 2013; 137 pp
This book is a quick but precise and careful introduction to the subject of functional analysis. It covers the basic topics that can be found in a basic graduate analysis text. But it also covers more sophisticated topics such as spectral theory, convexity, and fixed-point theorems. A special feature of the book is that it contains a great many examples and even some applications. It concludes with a statement and proof of Lomonosov's dramatic result about invariant subspaces.
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Table of Contents
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Chapters
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Chapter 1. Fundamentals
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Chapter 2. Ode to the Dual Space
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Chapter 3. Hilbert Space
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Chapter 4. The Algebra of Operators
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Chapter 5. Banach Algebra Basics
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Chapter 6. Topological Vector Spaces
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Chapter 7. Distributions
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Chapter 8. Spectral Theory
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Chapter 9. Convexity
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Chapter 10. Fixed-Point Theorems
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Additional Material
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Reviews
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This book is a short introduction to functional analysis along with a brief description of the most well known examples. It opens with a chapter on the mathematical fundamentals and then moves on to the primary examples. It is written at a level where the practicing mathematician or upper level graduate student can use it as a stand-alone resource to learn the basics of functional analysis. Proofs of all of the main theorems and propositions are included. Krantz has won many awards for his skill at expository writing and with this book he once again demonstrates that he deserves all of the accolades he receives.
Charles Ashbacher, Journal of Recreational Mathematics -
This book (barely over 100 pages of text) is very short...but nevertheless addresses most or all of the standard topics that one would expect to see in an introductory graduate-level semester in functional analysis, and perhaps even one or two things that might not get mentioned.
... Like other books in the Guide series, this one contains a good selection of examples, which I think is crucial. Another particularly nice feature of this book is the attention paid to applications of functional analysis, which even longer books frequently overlook. As some (non-exhaustive) examples, we see here, for example, the Uniform Boundedness theorem used to prove the existence of a broad class of functions with divergent Fourier series, the Hahn-Banach theorem invoked to establish the existence of the Green's function for smoothly bounded domains in the plane, and the contraction mapping principle used both to establish an existence-uniqueness theorem for differential equations and to give an elegant proof of the implicit function theorem.
... This book continues the tradition of high-quality expositions that have characterized every other Guide that I have looked at. This series in general, and this book in particular, deserve, and I hope will get, a wide audience.
Mark Hunacek, MAA Reviews
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RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
This book is a quick but precise and careful introduction to the subject of functional analysis. It covers the basic topics that can be found in a basic graduate analysis text. But it also covers more sophisticated topics such as spectral theory, convexity, and fixed-point theorems. A special feature of the book is that it contains a great many examples and even some applications. It concludes with a statement and proof of Lomonosov's dramatic result about invariant subspaces.
-
Chapters
-
Chapter 1. Fundamentals
-
Chapter 2. Ode to the Dual Space
-
Chapter 3. Hilbert Space
-
Chapter 4. The Algebra of Operators
-
Chapter 5. Banach Algebra Basics
-
Chapter 6. Topological Vector Spaces
-
Chapter 7. Distributions
-
Chapter 8. Spectral Theory
-
Chapter 9. Convexity
-
Chapter 10. Fixed-Point Theorems
-
This book is a short introduction to functional analysis along with a brief description of the most well known examples. It opens with a chapter on the mathematical fundamentals and then moves on to the primary examples. It is written at a level where the practicing mathematician or upper level graduate student can use it as a stand-alone resource to learn the basics of functional analysis. Proofs of all of the main theorems and propositions are included. Krantz has won many awards for his skill at expository writing and with this book he once again demonstrates that he deserves all of the accolades he receives.
Charles Ashbacher, Journal of Recreational Mathematics -
This book (barely over 100 pages of text) is very short...but nevertheless addresses most or all of the standard topics that one would expect to see in an introductory graduate-level semester in functional analysis, and perhaps even one or two things that might not get mentioned.
... Like other books in the Guide series, this one contains a good selection of examples, which I think is crucial. Another particularly nice feature of this book is the attention paid to applications of functional analysis, which even longer books frequently overlook. As some (non-exhaustive) examples, we see here, for example, the Uniform Boundedness theorem used to prove the existence of a broad class of functions with divergent Fourier series, the Hahn-Banach theorem invoked to establish the existence of the Green's function for smoothly bounded domains in the plane, and the contraction mapping principle used both to establish an existence-uniqueness theorem for differential equations and to give an elegant proof of the implicit function theorem.
... This book continues the tradition of high-quality expositions that have characterized every other Guide that I have looked at. This series in general, and this book in particular, deserve, and I hope will get, a wide audience.
Mark Hunacek, MAA Reviews