On the approximation of the differentiation operator by linear bounded operators on the class of twice differentiable functions in the space $L_2(0,\infty)$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 4, pp. 35-50
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We give an upper bound for the error of the best approximation of the (first-order) differentiation operator by linear bounded operators on the class of twice differentiable functions in the space $L_2(0,\infty)$. This upper bound is close to a known lower bound and improves the previous upper bounds. To prove the upper estimate, we consider a specific family of operators; in this family, we choose an operator that provides the least bound for the error of the best approximation.
Keywords:
Stechkin's problem, differential operator, half-line.
@article{TIMM_2012_18_4_a3,
author = {V. V. Arestov and M. A. Filatova},
title = {On the approximation of the differentiation operator by linear bounded operators on the class of twice differentiable functions in the space $L_2(0,\infty)$},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {35--50},
publisher = {mathdoc},
volume = {18},
number = {4},
year = {2012},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2012_18_4_a3/}
}
TY - JOUR AU - V. V. Arestov AU - M. A. Filatova TI - On the approximation of the differentiation operator by linear bounded operators on the class of twice differentiable functions in the space $L_2(0,\infty)$ JO - Trudy Instituta matematiki i mehaniki PY - 2012 SP - 35 EP - 50 VL - 18 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2012_18_4_a3/ LA - ru ID - TIMM_2012_18_4_a3 ER -
%0 Journal Article %A V. V. Arestov %A M. A. Filatova %T On the approximation of the differentiation operator by linear bounded operators on the class of twice differentiable functions in the space $L_2(0,\infty)$ %J Trudy Instituta matematiki i mehaniki %D 2012 %P 35-50 %V 18 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2012_18_4_a3/ %G ru %F TIMM_2012_18_4_a3
V. V. Arestov; M. A. Filatova. On the approximation of the differentiation operator by linear bounded operators on the class of twice differentiable functions in the space $L_2(0,\infty)$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 4, pp. 35-50. http://geodesic.mathdoc.fr/item/TIMM_2012_18_4_a3/