Optimal recovery of values of functions and their derivatives from inaccurate data on the Fourier transform
Sbornik. Mathematics, Tome 195 (2004) no. 10, pp. 1461-1476
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The problems of the optimal recovery of the derivatives of functions from inaccurate information about the Fourier transforms of these functions on a finite interval or the entire number line are considered. The Stechkin problem of the approximation of derivatives by bounded linear functionals, which is closely connected to this range of problems, is also studied. Precise Kolmogorov-type inequalities for derivatives corresponding to these problems are obtained.
@article{SM_2004_195_10_a2,
author = {G. G. Magaril-Il'yaev and K. Yu. Osipenko},
title = {Optimal recovery of values of functions and their derivatives from inaccurate data on the {Fourier} transform},
journal = {Sbornik. Mathematics},
pages = {1461--1476},
publisher = {mathdoc},
volume = {195},
number = {10},
year = {2004},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2004_195_10_a2/}
}
TY - JOUR AU - G. G. Magaril-Il'yaev AU - K. Yu. Osipenko TI - Optimal recovery of values of functions and their derivatives from inaccurate data on the Fourier transform JO - Sbornik. Mathematics PY - 2004 SP - 1461 EP - 1476 VL - 195 IS - 10 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SM_2004_195_10_a2/ LA - en ID - SM_2004_195_10_a2 ER -
%0 Journal Article %A G. G. Magaril-Il'yaev %A K. Yu. Osipenko %T Optimal recovery of values of functions and their derivatives from inaccurate data on the Fourier transform %J Sbornik. Mathematics %D 2004 %P 1461-1476 %V 195 %N 10 %I mathdoc %U http://geodesic.mathdoc.fr/item/SM_2004_195_10_a2/ %G en %F SM_2004_195_10_a2
G. G. Magaril-Il'yaev; K. Yu. Osipenko. Optimal recovery of values of functions and their derivatives from inaccurate data on the Fourier transform. Sbornik. Mathematics, Tome 195 (2004) no. 10, pp. 1461-1476. http://geodesic.mathdoc.fr/item/SM_2004_195_10_a2/