Geodesic
Density of Sums of Shifts of a Single Function in Hardy Spaces on the Half-Plane
Matematičeskie zametki, Tome 106 (2019) no. 5, pp. 669-678.

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It is proved that there exists a function defined in the closed upper half-plane for which the sums of its real shifts are dense in all Hardy spaces $H_{p}$ for $2 \le p \infty$, as well as in the space of functions analytic in the upper half-plane, continuous on its closure, and tending to zero at infinity.
Keywords: approximation, sums of shifts, density, Hardy spaces. 
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N. A. Dyuzhina. Density of Sums of Shifts of a Single Function in Hardy Spaces on the Half-Plane. Matematičeskie zametki, Tome 106 (2019) no. 5, pp. 669-678. http://geodesic.mathdoc.fr/item/MZM_2019_106_5_a2/

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