Geodesic
On best harmonic synthesis of periodic functions
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 5, pp. 155-174.

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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. 
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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/

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[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

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