ENGLISHRUSSIAN

Best approximation by linear superpositions (Approximate nomography)

By S. Ya. Khavinson

Book information

Publisher
American Mathematical Society
Year
1996
ISBN
0821804227, 9780821804223
Language
englishrussian
Format
DJVU
Filesize
1 MB (1448658 bytes)
Series
Translations of mathematical monographs 159
Pages
175\182
Library
kolxoz
Time added
2017-10-15 16:00:00
Approximation theory;Functions of several real var

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 Content: Discussing Kolmogorov's theorem Approximation of functions of two variables by sums $\varphi (X) + \psi (y)$ Problems of approximation by linear superpositions References.

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