Hardcover ISBN:  9780821804223 
Product Code:  MMONO/159 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470445744 
Product Code:  MMONO/159.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Hardcover ISBN:  9780821804223 
eBook: ISBN:  9781470445744 
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:  9780821804223 
Product Code:  MMONO/159 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470445744 
Product Code:  MMONO/159.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Hardcover ISBN:  9780821804223 
eBook ISBN:  9781470445744 
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 

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 HahnBanach theorem is emphasized. Also, considerable attention is given to the discussion of the DilibertoStraus 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.

Table of Contents

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


Reviews

A solid introduction to the theory of linear superpositions.
Journal of Approximation Theory


RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Reviews
 Requests
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 HahnBanach theorem is emphasized. Also, considerable attention is given to the discussion of the DilibertoStraus 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