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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2018, Volume 303, Pages 39–44
DOI: https://doi.org/10.1134/S0371968518040040 (Mi tm3940) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Density of sums of shifts of a single vector in sequence spaces

P. A. Borodin

Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991 Russia
Full-text PDF (164 kB) Citations (4)
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DOI: https://doi.org/10.1134/S0371968518040040
Abstract: We prove that in the real space l2(Z) of two-sided sequences there is an element such that the sums of its shifts are dense in all real spaces lp(Z), 2⩽p<∞, as well as in the real space c0(Z).
Keywords: shift, two-sided sequences, approximation, Fourier coefficients.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00333_а
Ministry of Education and Science of the Russian Federation НШ 6222.2018.1
The work was supported by the Russian Foundation for Basic Research (project no. 18-01-00333‑a) and by a grant of the President of the Russian Federation (project no. NSh-6222.2018.1).
Received: February 19, 2018
English version:
Proceedings of the Steklov Institute of Mathematics, 2018, Volume 303, Pages 31–35
DOI: https://doi.org/10.1134/S0081543818080047
Bibliographic databases:
Document Type: Article
UDC: 517.982.256
MSC: 41A65, 46B20, 46B25
Language: Russian
Citation: P. A. Borodin, “Density of sums of shifts of a single vector in sequence spaces”, Harmonic analysis, approximation theory, and number theory, Collected papers. Dedicated to Academician Sergei Vladimirovich Konyagin on the occasion of his 60th birthday, Trudy Mat. Inst. Steklova, 303, MAIK Nauka/Interperiodica, Moscow, 2018, 39–44; Proc. Steklov Inst. Math., 303 (2018), 31–35
Citation in format AMSBIB
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\paper Density of sums of shifts of a single vector in sequence spaces
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\bookinfo Collected papers. Dedicated to Academician Sergei Vladimirovich Konyagin on the occasion of his 60th birthday
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\vol 303
\pages 39--44
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    • This publication is cited in the following 4 articles:
    1. Yu. A. Skvortsov, “Plotnost summ sdvigov odnoi funktsii dlya deistviya kompaktnoi gruppy”, Matem. zametki, 117:3 (2025), 479–482  mathnet  crossref
    2. N. A. Dyuzhina, “Density of the sums of shifts of a single function in the L02 space on a compact Abelian group”, Sb. Math., 215:6 (2024), 743–754  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. N. A. Dyuzhina, “Multidimensional Analogs of Theorems about the Density of Sums of Shifts of a Single Function”, Math. Notes, 113:5 (2023), 731–735  mathnet  crossref  crossref  mathscinet
    4. P. A. Borodin, K. S. Shklyaev, “Density of quantized approximations”, Russian Math. Surveys, 78:5 (2023), 797–851  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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