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// Trudy Matematicheskogo Instituta imeni V.A. Steklova
// Archive
Trudy Mat. Inst. Steklova,
2018
Volume 303,
Pages
39–44
(Mi tm3940)
This article is cited 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
Abstract:
We prove that in the real space
$l_2(\mathbb Z)$
of two-sided sequences there is an element such that the sums of its shifts are dense in all real spaces
$l_p(\mathbb Z)$
,
$2\le p<\infty $
, as well as in the real space
$c_0(\mathbb Z)$
.
Keywords:
shift, two-sided sequences, approximation, Fourier coefficients.
UDC:
517.982.256
MSC:
41A65
,
46B20
,
46B25
Received:
February 19, 2018
DOI:
10.1134/S0371968518040040
Fulltext:
PDF file (164 kB)
References
Cited by
English version:
Proceedings of the Steklov Institute of Mathematics, 2018,
303
,
31–35
Bibliographic databases:
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Steklov Math. Inst. of RAS
, 2025