# Constructive theory of functions

A concept introduced by S.N. Bernshtein, who called the constructive theory of functions "a branch of the theory of functions aiming at a most simple and convenient foundation for the qualitative study and computation both of empirical functions as well as of any function that is a solution of a naturally posed problem in mathematical analysis" . It should be noted that the constructive theory of functions includes the theory of approximation of functions as one of its branches. However, the practical use of the phrase "the constructive theory of functions" gained a more narrow meaning as another name for the theory of approximation of functions. Nowadays the phrase "the constructive theory of functions" is seldom used.

#### References

[1a] | S.N. Bernshtein, Izv. Akad. Nauk SSSR Ser. Mat. , 9 : 3 (1945) pp. 145–158 |

[1b] | S.N. Bernshtein, "Collected works" , 2 , Moscow (1954) pp. 349–360 (In Russian) |

#### Comments

#### References

[a1] | I.I. Ibragimov, "On Bernstein's contributions to the constructive theory of functions" G. Alexits (ed.) S.B. Stechkin (ed.) , Proc. Conf. Constructive Theory of Functions , Akad. Kindó (1969) pp. 27–40 (In Russian) |

[a2] | G.P. Szegö, "The contributions of L. Fejér to the constructive function theory" G. Alexits (ed.) S.B. Stechkin (ed.) , Proc. Conf. Constructive Theory of Functions , Akad. Kindó (1969) pp. 19–26 |

**How to Cite This Entry:**

Constructive theory of functions. S.A. Telyakovskii (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Constructive_theory_of_functions&oldid=16563