Geodesic
On best harmonic synthesis of periodic functions
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 5, pp. 155-174 
G. G. Magaril-Il'yaev; K. Yu. Osipenko. On best harmonic synthesis of periodic functions. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 5, pp. 155-174. http://geodesic.mathdoc.fr/item/FPM_2013_18_5_a8/
@article{FPM_2013_18_5_a8,
     author = {G. G. Magaril-Il'yaev and K. Yu. Osipenko},
     title = {On best harmonic synthesis of periodic functions},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {155--174},
     year = {2013},
     volume = {18},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2013_18_5_a8/}
}
TY  - JOUR
AU  - G. G. Magaril-Il'yaev
AU  - K. Yu. Osipenko
TI  - On best harmonic synthesis of periodic functions
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2013
SP  - 155
EP  - 174
VL  - 18
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/FPM_2013_18_5_a8/
LA  - ru
ID  - FPM_2013_18_5_a8
ER  - 
%0 Journal Article
%A G. G. Magaril-Il'yaev
%A K. Yu. Osipenko
%T On best harmonic synthesis of periodic functions
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2013
%P 155-174
%V 18
%N 5
%U http://geodesic.mathdoc.fr/item/FPM_2013_18_5_a8/
%G ru
%F FPM_2013_18_5_a8

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

In this paper, we construct optimal methods of recovery of periodic functions from a known (exact or inexact) finite family of their Fourier coefficients. The proposed approach to constructing recovery methods is compared with the approach based on the Tikhonov regularization method.

[1] Ilin V. A., Poznyak E. G., Osnovy matematicheskogo analiza, Ch. II, Nauka, M., 1973

[2] Magaril-Ilyaev G. G., Osipenko K. Yu., “Optimalnoe vosstanovlenie funktsii i ikh proizvodnykh po koeffitsientam Fure, zadannym s pogreshnostyu”, Mat. sb., 193:3 (2002), 79–100 | DOI | MR | Zbl

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

[4] Magaril-Ilyaev G. G., Osipenko K. Yu., “Optimalnoe vosstanovlenie znachenii funktsii i ikh proizvodnykh po netochno zadannomu preobrazovaniyu Fure”, Mat. sb., 195:10 (2004), 67–82 | DOI | MR | Zbl

[5] Magaril-Ilyaev G. G., Osipenko K. Yu., “Ob optimalnom garmonicheskom sinteze po netochno zadannomu spektru”, Funkts. analiz i ego pril., 44:3 (2010), 76–79 | DOI | MR | Zbl

[6] Magaril-Ilyaev G. G., Osipenko K. Yu., “Kak nailuchshim obrazom vosstanovit funktsiyu po netochno zadannomu spektru”, Mat. zametki, 92:1 (2012), 59–67 | DOI | MR | Zbl

[7] Magaril-Ilyaev G. G., Sivkova E. O., “Nailuchshee vosstanovlenie operatora Laplasa funktsii po eë netochno zadannomu spektru”, Mat. sb., 203:4 (2012), 119–130 | DOI | MR | Zbl

[8] Sivkova E. O., “Ob optimalnom vosstanovlenii laplasiana funktsii po eë netochno zadannomu preobrazovaniyu Fure”, Vladikavkaz. mat. zhurn., 14:4 (2012), 63–72 | MR