Sbornik. Mathematics, Tome 52 (1985) no. 2, pp. 553-555
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S. V. Kolesnikov. On a theorem of M. V. Keldysh concerning pointwise convergence of a sequence of polynomials. Sbornik. Mathematics, Tome 52 (1985) no. 2, pp. 553-555. http://geodesic.mathdoc.fr/item/SM_1985_52_2_a14/
@article{SM_1985_52_2_a14,
author = {S. V. Kolesnikov},
title = {On a~theorem of {M.} {V.~Keldysh} concerning pointwise convergence of a~sequence of polynomials},
journal = {Sbornik. Mathematics},
pages = {553--555},
year = {1985},
volume = {52},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1985_52_2_a14/}
}
TY - JOUR
AU - S. V. Kolesnikov
TI - On a theorem of M. V. Keldysh concerning pointwise convergence of a sequence of polynomials
JO - Sbornik. Mathematics
PY - 1985
SP - 553
EP - 555
VL - 52
IS - 2
UR - http://geodesic.mathdoc.fr/item/SM_1985_52_2_a14/
LA - en
ID - SM_1985_52_2_a14
ER -
%0 Journal Article
%A S. V. Kolesnikov
%T On a theorem of M. V. Keldysh concerning pointwise convergence of a sequence of polynomials
%J Sbornik. Mathematics
%D 1985
%P 553-555
%V 52
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1985_52_2_a14/
%G en
%F SM_1985_52_2_a14
This article contains a proof of the following fact: for any bounded function $f(z)$, $|z|=1$, of the first Baire class such that $\int_{|z|=1}f(z)z^n\,dz=0$ for $n=0,1,\dots$, there exists a uniformly bounded sequence of polynomials on $|z|=1$ converging pointwise to $f(z)$. Bibliography: 2 titles.
