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Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2014, Number 5, Pages 35–40 (Mi vmumm347)  

This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

Bases of trigonometric polynomials consisting of shifts of Dirichlet kernels

T. P. Lukashenko

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The system of shifts of Dirichlet kernel on $\frac{2k\pi}{2n+1}$, $k=0,\pm1,…,\pm n$, and the system of such shifts of the conjugate Dirichlet kernel with $\frac12$ are orthogonal bases in the space of trigonometric polynomials of degree $n$. The system of shifts of kernels $\sum_{k=m}^n \cos kx$ and $\sum_{k=m}^n\sin kx$ on $\frac{2k\pi}{n-m+1}$, $k=0,1,…,n-m$, is an orthogonal basis in the space of trigonometric polynomials with the components from $m\geqslant1$$n$. There is no orthogonal basis of shifts of any function in this space for $0<m<n$.

Key words: orthogonal basis, trigonometric polynomials, Dirichlet kernel, conjugate Dirichlet kernel.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 11.G34.31.0054
ГК 02.G25.31.0030
ГК 02.G36.31.0006
НШ-1096.2014.1
Russian Foundation for Basic Research 14-01-00417


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English version:
Moscow University Mathematics Bulletin, 2014, 69:5, 211–216

Bibliographic databases:

UDC: 517.518
Received: 25.09.2013

Citation: T. P. Lukashenko, “Bases of trigonometric polynomials consisting of shifts of Dirichlet kernels”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2014, no. 5, 35–40; Moscow University Mathematics Bulletin, 69:5 (2014), 211–216

Citation in format AMSBIB
\Bibitem{Luk14}
\by T.~P.~Lukashenko
\paper Bases of trigonometric polynomials consisting of shifts of Dirichlet kernels
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2014
\issue 5
\pages 35--40
\mathnet{http://mi.mathnet.ru/vmumm347}
\transl
\jour Moscow University Mathematics Bulletin
\yr 2014
\vol 69
\issue 5
\pages 211--216
\crossref{https://doi.org/10.3103/S0027132214050064}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84926664674}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Fadeeva, “Parseval frames of serial shifts of a function in spaces of trigonometric polynomials”, Moscow University Mathematics Bulletin, 73:6 (2018), 239–244  mathnet  crossref  isi
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