| Softcover ISBN: | 978-1-4704-4116-6 |
| Product Code: | STML/85 |
| 219 pp | |
| List Price: | $52.00 |
| Individual Price: | $41.60 |
| Electronic ISBN: | 978-1-4704-4733-5 |
| Product Code: | STML/85.E |
| 219 pp | |
| List Price: | $52.00 |
| Individual Price: | $41.60 |
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Book DetailsStudent Mathematical LibraryVolume: 85; 2018MSC: Primary 46; 45;
This book introduces functional analysis to undergraduate mathematics students who possess a basic background in analysis and linear algebra. By studying how the Volterra operator acts on vector spaces of continuous functions, its readers will sharpen their skills, reinterpret what they already know, and learn fundamental Banach-space techniques—all in the pursuit of two celebrated results: the Titchmarsh Convolution Theorem and the Volterra Invariant Subspace Theorem. Exercises throughout the text enhance the material and facilitate interactive study.
ReadershipUndergraduate students interested in functional analysis and operator theory.
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Table of Contents
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From Volterra to Banach
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Starting out
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Springing ahead
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Springing higher
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Operators as points
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Travels with Titchmarsh
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The Titchmarsh convolution theorem
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Titchmarsh finale
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Invariance through duality
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Invariant subspaces
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Digging into duality
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Rendezvous with Riez
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V-invariance: Finale
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Uniform convergence
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$\mathbb {C}$omplex primer
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Uniform approximation by polynomials
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Riemann-Stieltjes primer
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Additional Material
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Reviews
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I would recommend this book to anyone seeking a pleasant read on functional analysis. The book elegantly and clearly traverses the varied paths of mathematics (algebraic and analytical, real and complex, finite and transfinite), gently leading the reader to profound and relevant results of modern analysis.
Daniel M. Pellegrino, Mathematical Reviews -
The author has worked hard to make these topics accessible to undergraduates who have taken (good) courses in linear algebra and real analysis...The exposition is, throughout the book, of very high quality. Shapiro is a talented writer, and he knows how to explain things clearly and engagingly, in easily-digested pieces for an undergraduate audience...it will offer students an accessible, stimulating, and informative look at a beautiful branch of mathematics.
Mark Hunacek, MAA Reviews
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This book introduces functional analysis to undergraduate mathematics students who possess a basic background in analysis and linear algebra. By studying how the Volterra operator acts on vector spaces of continuous functions, its readers will sharpen their skills, reinterpret what they already know, and learn fundamental Banach-space techniques—all in the pursuit of two celebrated results: the Titchmarsh Convolution Theorem and the Volterra Invariant Subspace Theorem. Exercises throughout the text enhance the material and facilitate interactive study.
Undergraduate students interested in functional analysis and operator theory.
-
From Volterra to Banach
-
Starting out
-
Springing ahead
-
Springing higher
-
Operators as points
-
Travels with Titchmarsh
-
The Titchmarsh convolution theorem
-
Titchmarsh finale
-
Invariance through duality
-
Invariant subspaces
-
Digging into duality
-
Rendezvous with Riez
-
V-invariance: Finale
-
Uniform convergence
-
$\mathbb {C}$omplex primer
-
Uniform approximation by polynomials
-
Riemann-Stieltjes primer
-
I would recommend this book to anyone seeking a pleasant read on functional analysis. The book elegantly and clearly traverses the varied paths of mathematics (algebraic and analytical, real and complex, finite and transfinite), gently leading the reader to profound and relevant results of modern analysis.
Daniel M. Pellegrino, Mathematical Reviews -
The author has worked hard to make these topics accessible to undergraduates who have taken (good) courses in linear algebra and real analysis...The exposition is, throughout the book, of very high quality. Shapiro is a talented writer, and he knows how to explain things clearly and engagingly, in easily-digested pieces for an undergraduate audience...it will offer students an accessible, stimulating, and informative look at a beautiful branch of mathematics.
Mark Hunacek, MAA Reviews
