Approximation of the Hardy--Sobolev class of functions analytic in a~half-plane by entire functions of exponential type
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 4, pp. 18-30
Voir la notice de l'article provenant de la source Math-Net.Ru
We study the value $\mathcal E_\sigma(H^p_n)_{H^p}$ of the best approximation in the norm of the Hardy space $H^p$ for $1\le p\le\infty$ of the Hardy–Sobolev class $H_n^p$ of functions analytic in a half-plane with bounded $H^p$-norm of the $n$th-order derivative by entire functions of exponential type not exceeding $\sigma$. The equality $\mathcal E_\sigma(H^p_n)_{H^p}=\sigma^{-n}$ is proved. A linear method providing the best approximation of the class is constructed.
Keywords:
Hardy class, approximation of functions, entire functions of exponential type.
@article{TIMM_2010_16_4_a1,
author = {R. R. Akopyan},
title = {Approximation of the {Hardy--Sobolev} class of functions analytic in a~half-plane by entire functions of exponential type},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {18--30},
publisher = {mathdoc},
volume = {16},
number = {4},
year = {2010},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2010_16_4_a1/}
}
TY - JOUR AU - R. R. Akopyan TI - Approximation of the Hardy--Sobolev class of functions analytic in a~half-plane by entire functions of exponential type JO - Trudy Instituta matematiki i mehaniki PY - 2010 SP - 18 EP - 30 VL - 16 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2010_16_4_a1/ LA - ru ID - TIMM_2010_16_4_a1 ER -
%0 Journal Article %A R. R. Akopyan %T Approximation of the Hardy--Sobolev class of functions analytic in a~half-plane by entire functions of exponential type %J Trudy Instituta matematiki i mehaniki %D 2010 %P 18-30 %V 16 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2010_16_4_a1/ %G ru %F TIMM_2010_16_4_a1
R. R. Akopyan. Approximation of the Hardy--Sobolev class of functions analytic in a~half-plane by entire functions of exponential type. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 4, pp. 18-30. http://geodesic.mathdoc.fr/item/TIMM_2010_16_4_a1/