Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 14, Tome 215 (1994), pp. 217-225
Citer cet article
Yu. V. Netrusov. An intrinsic description of functions defined on a plane convex domain and having a prescribed order approximation by algebraic polynomials. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 14, Tome 215 (1994), pp. 217-225. http://geodesic.mathdoc.fr/item/ZNSL_1994_215_a13/
@article{ZNSL_1994_215_a13,
author = {Yu. V. Netrusov},
title = {An intrinsic description of functions defined on a~plane convex domain and having a~prescribed order approximation by algebraic polynomials},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {217--225},
year = {1994},
volume = {215},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_215_a13/}
}
TY - JOUR
AU - Yu. V. Netrusov
TI - An intrinsic description of functions defined on a plane convex domain and having a prescribed order approximation by algebraic polynomials
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1994
SP - 217
EP - 225
VL - 215
UR - http://geodesic.mathdoc.fr/item/ZNSL_1994_215_a13/
LA - ru
ID - ZNSL_1994_215_a13
ER -
%0 Journal Article
%A Yu. V. Netrusov
%T An intrinsic description of functions defined on a plane convex domain and having a prescribed order approximation by algebraic polynomials
%J Zapiski Nauchnykh Seminarov POMI
%D 1994
%P 217-225
%V 215
%U http://geodesic.mathdoc.fr/item/ZNSL_1994_215_a13/
%G ru
%F ZNSL_1994_215_a13
Let $0<\alpha$, $0, $m$ a positive integer, let $f$ a function defined on a plane convex domain $G$. Denote by $E_m(f,L_p(G))$ the best approximation of $f$ in $L_p(G)$ by algebraic polynomials of degree $m$. A description of functions $f\in L_p(G)$ such that inequalities hold $$ E_m(f,L_p(G))\le Cm^{-\alpha},\qquad m=1,2,\dots, $$ is given. Bibliography: 7 titles.
