Translations of Mathematical Monographs 1997; 175 pp; hardcover Volume: 159 ISBN10: 0821804227 ISBN13: 9780821804223 List Price: US$95 Member Price: US$76 Order Code: MMONO/159
 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. Readership Graduate students and mathematicians working in approximation theory and constructive function theory, and functional analysts working in deep and nontrivial applications. Reviews "A solid introduction to the theory of linear superpositions."  Journal of Approximation Theory Table of Contents  Discussing Kolmogorov's theorem
 Approximation of functions of two variables by sums \(\varphi (x) + \psi (y)\)
 Problems of approximation by linear superpositions
 References
