Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 21, Tome 206 (1993), pp. 151-173
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N. A. Shirokov. A direct theorem for strictly convex domains in $\mathbb C^n$. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 21, Tome 206 (1993), pp. 151-173. http://geodesic.mathdoc.fr/item/ZNSL_1993_206_a12/
@article{ZNSL_1993_206_a12,
author = {N. A. Shirokov},
title = {A direct theorem for strictly convex domains in~$\mathbb C^n$},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {151--173},
year = {1993},
volume = {206},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1993_206_a12/}
}
TY - JOUR
AU - N. A. Shirokov
TI - A direct theorem for strictly convex domains in $\mathbb C^n$
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1993
SP - 151
EP - 173
VL - 206
UR - http://geodesic.mathdoc.fr/item/ZNSL_1993_206_a12/
LA - ru
ID - ZNSL_1993_206_a12
ER -
%0 Journal Article
%A N. A. Shirokov
%T A direct theorem for strictly convex domains in $\mathbb C^n$
%J Zapiski Nauchnykh Seminarov POMI
%D 1993
%P 151-173
%V 206
%U http://geodesic.mathdoc.fr/item/ZNSL_1993_206_a12/
%G ru
%F ZNSL_1993_206_a12
For a strictly convex $C^2$-domain $\Omega\subset\mathbb C^n$ and a function $f\in\Lambda^a(\Omega)$ holomorphic in $\Omega$, we construct polynomials $P_n$, $\deg P_n\le N$, such that $|f(z)-P_n(z)|\le CN^{-a}$, $z\in\overline\Omega$. Bibliography: 12 titles.
