Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2018, Number 6, Pages 30–36 (Mi vmumm581)  
This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

Parseval frames of serial shifts of a function in spaces of trigonometric polynomials

A. V. Fadeeva

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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Abstract: The work establishes possible dimensions of Parseval's frame in the space of trigonometric polynomials of the form $T_Q(x)=\sum\limits_{k\in Q}c_k e^{ikx}$ consisting of serial translations of a polynomial ($c_k\in\mathbb C$, where the finite set $Q\subset\mathbb Z$). Sufficient and necessary conditions for a system of serial translations to be a Parseval's frame are also established there. The result is applied to some particular cases.
Key words: the Parseval's frame, space of trigonometric polynomials, shifts of functions.
Received: 27.04.2018
English version:
Moscow University Mathematics Bulletin, 2018, Volume 73, Issue 6, Pages 239–244
DOI: https://doi.org/10.3103/S0027132218060049
Bibliographic databases:
Document Type: Article
UDC: 517.98, 517.51
Language: Russian
Citation: A. V. Fadeeva, “Parseval frames of serial shifts of a function in spaces of trigonometric polynomials”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2018, no. 6, 30–36; Moscow University Mathematics Bulletin, 73:6 (2018), 239–244
Citation in format AMSBIB
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