Geodesic
On optimal recovery of the operator of $k$-th divided difference from its inaccurately given Fourier transform
Vladikavkazskij matematičeskij žurnal, Tome 17 (2015) no. 3, pp. 84-92 
S. A. Unuchek. On optimal recovery of the operator of $k$-th divided difference from its inaccurately given Fourier transform. Vladikavkazskij matematičeskij žurnal, Tome 17 (2015) no. 3, pp. 84-92. http://geodesic.mathdoc.fr/item/VMJ_2015_17_3_a9/
@article{VMJ_2015_17_3_a9,
     author = {S. A. Unuchek},
     title = {On optimal recovery of the operator of $k$-th divided difference from its inaccurately given {Fourier} transform},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {84--92},
     year = {2015},
     volume = {17},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2015_17_3_a9/}
}
TY  - JOUR
AU  - S. A. Unuchek
TI  - On optimal recovery of the operator of $k$-th divided difference from its inaccurately given Fourier transform
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2015
SP  - 84
EP  - 92
VL  - 17
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VMJ_2015_17_3_a9/
LA  - ru
ID  - VMJ_2015_17_3_a9
ER  - 
%0 Journal Article
%A S. A. Unuchek
%T On optimal recovery of the operator of $k$-th divided difference from its inaccurately given Fourier transform
%J Vladikavkazskij matematičeskij žurnal
%D 2015
%P 84-92
%V 17
%N 3
%U http://geodesic.mathdoc.fr/item/VMJ_2015_17_3_a9/
%G ru
%F VMJ_2015_17_3_a9

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper considers the recovery problem of the $k$-th divided difference of sequence, provided that the Fourier transform of this sequence on the interval is approximately known. The optimal recovery method is also constructed.

[1] Smolyak S. A., Ob optimalnom vosstanovlenii funktsii i funktsionalov ot nikh, Dis. $\dots$ kand. fiz.-mat. nauk, MGU, M., 1965

[2] Kolmogorov A. N., Izbrannye trudy. Matematika i mekhanika, Nauka, M., 1985, 470 pp. | MR

[3] Nikolskii S. M., “K voprosu ob otsenkakh priblizhenii kvadraturnymi formulami”, Uspekhi mat. nauk, 5:2 (1950), 165–177 | MR | Zbl

[4] Marchuk A. G., Osipenko K. Yu., “Nailuchshee priblizhenie funktsii, zadannykh s pogreshnostyu v konechnom chisle tochek”, Mat. zametki, 17:3 (1975), 359–368 | MR | Zbl

[5] Unuchek S. A., “Optimalnoe vosstanovlenie razdelennykh raznostei po netochno zadannoi posledovatelnosti”, Dif. uravneniya (to appear)

[6] Magaril-Ilyaev G. G., Osipenko K. Yu., “Optimalnoe vosstanovlenie funktsii i ikh proizvodnykh po priblizhennoi informatsii o spektre i neravenstva dlya proizvodnykh”, Funktsion. analiz i ego pril., 37:3 (2003), 51–64 | DOI | MR | Zbl

[7] Magaril-Ilyaev G. G., Osipenko K. Yu., “Neravenstvo Khardi–Littlvuda–Polia i vosstanovlenie proizvodnykh po netochnoi informatsii”, Dokl. RAN, 438:3 (2011), 300–302 | MR | Zbl