Email this article Exactness and optimality of methods for recovering functions from their spectrum
- Authors: Magaril-Il’yaev G.G.1,2,3, Osipenko K.Y.1,2,4
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Affiliations:
- Faculty of Mechanics and Mathematics
- Institute for Information Transmission Problems (Kharkevich Institute)
- Peoples’ Friendship University of Russia
- Moscow Aviation Institute (National Research University)
- Issue: Vol 293, No 1 (2016)
- Pages: 194-208
- Section: Article
- URL: https://journals.rcsi.science/0081-5438/article/view/173734
- DOI: https://doi.org/10.1134/S0081543816040143
- ID: 173734
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Abstract
Optimal methods are constructed for recovering functions and their derivatives in a Sobolev class of functions on the line from exactly or approximately defined Fourier transforms of these functions on an arbitrary measurable set. The methods are exact on certain subspaces of entire functions. Optimal recovery methods are also constructed for wider function classes obtained as the sum of the original Sobolev class and a subspace of entire functions.
About the authors
G. G. Magaril-Il’yaev
Faculty of Mechanics and Mathematics; Institute for Information Transmission Problems (Kharkevich Institute); Peoples’ Friendship University of Russia
Author for correspondence.
Email: magaril@mech.math.msu.su
Russian Federation, Moscow, 119991; Bol’shoi Karetnyi per. 19, str. 1, Moscow, 127051; ul. Miklukho-Maklaya 6, Moscow, 117198
K. Yu. Osipenko
Faculty of Mechanics and Mathematics; Institute for Information Transmission Problems (Kharkevich Institute); Moscow Aviation Institute (National Research University)
Email: magaril@mech.math.msu.su
Russian Federation, Moscow, 119991; Bol’shoi Karetnyi per. 19, str. 1, Moscow, 127051; Volokolamskoe sh. 4, Moscow, 125993
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