| Hardcover ISBN: | 978-0-8218-0422-3 |
| Product Code: | MMONO/159 |
| List Price: | $165.00 |
| MAA Member Price: | $148.50 |
| AMS Member Price: | $132.00 |
| eBook ISBN: | 978-1-4704-4574-4 |
| Product Code: | MMONO/159.E |
| List Price: | $155.00 |
| MAA Member Price: | $139.50 |
| AMS Member Price: | $124.00 |
| Hardcover ISBN: | 978-0-8218-0422-3 |
| eBook: ISBN: | 978-1-4704-4574-4 |
| Product Code: | MMONO/159.B |
| List Price: | $320.00 $242.50 |
| MAA Member Price: | $288.00 $218.25 |
| AMS Member Price: | $256.00 $194.00 |
| Hardcover ISBN: | 978-0-8218-0422-3 |
| Product Code: | MMONO/159 |
| List Price: | $165.00 |
| MAA Member Price: | $148.50 |
| AMS Member Price: | $132.00 |
| eBook ISBN: | 978-1-4704-4574-4 |
| Product Code: | MMONO/159.E |
| List Price: | $155.00 |
| MAA Member Price: | $139.50 |
| AMS Member Price: | $124.00 |
| Hardcover ISBN: | 978-0-8218-0422-3 |
| eBook ISBN: | 978-1-4704-4574-4 |
| Product Code: | MMONO/159.B |
| List Price: | $320.00 $242.50 |
| MAA Member Price: | $288.00 $218.25 |
| AMS Member Price: | $256.00 $194.00 |
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Book DetailsTranslations of Mathematical MonographsVolume: 159; 1997; 175 ppMSC: Primary 41
This book deals with problems of approximation of continuous or bounded functions of several variables by linear superposition of functions that are from the same class and have fewer variables. The main topic is the space of linear superpositions \(D\) considered as a subspace of the space of continuous functions \(C(X)\) on a compact space \(X\). Such properties as density of \(D\) in \(C(X)\), its closedness, proximality, etc. are studied in great detail. The approach to these and other problems based on duality and the Hahn-Banach theorem is emphasized. Also, considerable attention is given to the discussion of the Diliberto-Straus algorithm for finding the best approximation of a given function by linear superpositions.
ReadershipGraduate students and mathematicians working in approximation theory and constructive function theory, and functional analysts working in deep and nontrivial applications.
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Table of Contents
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Chapters
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Introduction
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Chapter 1. Discussing Kolmogorov’s theorem
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Chapter 2. Approximation of functions of two variables by sums $\varphi (x) + \psi $
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Chapter 3. Problems of approximation by linear superpositions
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Reviews
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A solid introduction to the theory of linear superpositions.
Journal of Approximation Theory
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This book deals with problems of approximation of continuous or bounded functions of several variables by linear superposition of functions that are from the same class and have fewer variables. The main topic is the space of linear superpositions \(D\) considered as a subspace of the space of continuous functions \(C(X)\) on a compact space \(X\). Such properties as density of \(D\) in \(C(X)\), its closedness, proximality, etc. are studied in great detail. The approach to these and other problems based on duality and the Hahn-Banach theorem is emphasized. Also, considerable attention is given to the discussion of the Diliberto-Straus algorithm for finding the best approximation of a given function by linear superpositions.
Graduate students and mathematicians working in approximation theory and constructive function theory, and functional analysts working in deep and nontrivial applications.
-
Chapters
-
Introduction
-
Chapter 1. Discussing Kolmogorov’s theorem
-
Chapter 2. Approximation of functions of two variables by sums $\varphi (x) + \psi $
-
Chapter 3. Problems of approximation by linear superpositions
-
A solid introduction to the theory of linear superpositions.
Journal of Approximation Theory
