Constructive Theory of Functions

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Constructive Theory of Functions


a branch of the theory of functions in which both approximate representations of functions and the functions themselves are studied proceeding from the properties of their approximate representations. The constructive theory of functions took shape as an independent discipline in the works of S. N. Bernshtein (the term “constructive theory of functions” is ascribed to him as well), who proceeded from the ideas of P. L. Chebyshev related to the best approximations of functions, interpolation by the method of least squares, and the problem of moments.


Bernshtein, S. N. Sobr. soch., vol. 1: Konstruktivnaia teoriia funktsii [1905–30]. Moscow, 1952.
Natanson, I. P. Konstruktivnaia teoriia funktsii. Moscow-Leningrad, 1949.
Smirnov, V. I., and N. A. Lebedev. Konstruktivnaia teoriia funktsii kompleksnogo peremennogo. Moscow-Leningrad, 1964.
The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
Now Sinc approximations are widely used in various parts of constructive theory of functions, computational mathematics, in solving ordinary differential equations and partial differential equations, in signal processing, and other engineering calculations.

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