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 Hp for 2⩽p<∞, 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.
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
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\by N.~A.~Dyuzhina
\paper Density of Sums of Shifts of a Single Function in Hardy Spaces on the Half-Plane
\jour Mat. Zametki
\yr 2019
\vol 106
\issue 5
\pages 669--678
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\jour Math. Notes
\yr 2019
\vol 106
\issue 5
\pages 711--719
\crossref{https://doi.org/10.1134/S0001434619110051}
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Linking options:
https://www.mathnet.ru/eng/mzm12262
https://doi.org/10.4213/mzm12262
https://www.mathnet.ru/eng/mzm/v106/i5/p669
This publication is cited in the following 2 articles:
P. A. Borodin, K. S. Shklyaev, “Density of quantized approximations”, Russian Math. Surveys, 78:5 (2023), 797–851
N. A. Dyuzhina, “Density of Derivatives of Simple Partial Fractions in Hardy Spaces in the Half-Plane”, Math. Notes, 109:1 (2021), 46–53
Citation in format AMSBIB
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