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JOURNALS // 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


 English version:
Proceedings of the Steklov Institute of Mathematics, 2018, 303, 31–35

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