ENGLISH

Best Approximation by Linear Superpositions (Approximate Nomography)

By S. Ya. Khavinson

Book information

Publisher
American Mathematical Society
Year
1996
ISBN
0821804227, 9780821804223
Language
english
Format
PDF
Filesize
15 MB (15879886 bytes)
Series
Translations of Mathematical Monographs
Pages
175\188
Time added
2016-03-26 17:20:38

Description

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.

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