Geodesic
Probabilistic proof of a theorem of A.\,O.~Gel'fond
Izvestiya. Mathematics , Tome 1 (1967) no. 6, pp. 1323-1329

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we present a proof of a theorem of A. O. Gel'fond on the approximation of a continuous function by its generalized Bern?teĭn polynomials, our proof being based on probability theory. Our proof consists in interpreting a generalized Bern?teĭn polynomial as the mathematical expectation of a function of a specially chosen random variable, followed by the use of elementary theorems of probability theory. In view of the fact that in the new proof we give no direct estimate of the function's deviation from its polynomials, the traditional arguments of the constructive theory of functions are markedly simplified. 
@article{IM2_1967_1_6_a10,
     author = {A. A. Shahbazov},
     title = {Probabilistic proof of a theorem of {A.\,O.~Gel'fond}},
     journal = {Izvestiya. Mathematics },
     pages = {1323--1329},
     publisher = {mathdoc},
     volume = {1},
     number = {6},
     year = {1967},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1967_1_6_a10/}
}
TY  - JOUR
AU  - A. A. Shahbazov
TI  - Probabilistic proof of a theorem of A.\,O.~Gel'fond
JO  - Izvestiya. Mathematics 
PY  - 1967
SP  - 1323
EP  - 1329
VL  - 1
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1967_1_6_a10/
LA  - en
ID  - IM2_1967_1_6_a10
ER  - 
%0 Journal Article
%A A. A. Shahbazov
%T Probabilistic proof of a theorem of A.\,O.~Gel'fond
%J Izvestiya. Mathematics 
%D 1967
%P 1323-1329
%V 1
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1967_1_6_a10/
%G en
%F IM2_1967_1_6_a10
A. A. Shahbazov. Probabilistic proof of a theorem of A.\,O.~Gel'fond. Izvestiya. Mathematics , Tome 1 (1967) no. 6, pp. 1323-1329. http://geodesic.mathdoc.fr/item/IM2_1967_1_6_a10/