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Mat. Zametki, 2019, Volume 106, Issue 5, Pages 669–678 (Mi mz12262)  

Density of Sums of Shifts of a Single Function in Hardy Spaces on the Half-Plane

N. A. Dyuzhina

Lomonosov Moscow State University

Abstract: 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.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00333а
This work was supported by the Russian Foundation for Basic Research under grant 18-01-00333a.


DOI: https://doi.org/10.4213/mzm12262

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English version:
Mathematical Notes, 2019, 106:5, 711–719

Bibliographic databases:

UDC: 517.547.54+517.982.256
Received: 25.11.2018
Revised: 29.03.2019

Citation: N. A. Dyuzhina, “Density of Sums of Shifts of a Single Function in Hardy Spaces on the Half-Plane”, Mat. Zametki, 106:5 (2019), 669–678; Math. Notes, 106:5 (2019), 711–719

Citation in format AMSBIB
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\pages 669--678
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