Constructive Theory of Functions

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.

REFERENCES

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.
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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