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Izv. Vyssh. Uchebn. Zaved. Mat., 2019, Number 2, Pages 57–68 (Mi ivm9440)  

On existence of frames based on the Szegö kernel in the Hardy space

K. S. Speransky, P. A. Terekhin

Saratov State University, 83 Astrakhanskaya str., Saratov, 410012 Russia

Abstract: It is well-known that a sequence of functions constructed by sampling of the Szegö kernel cannot be the Duffin–Shaeffer frame for the Hardy space on the unit disk. In this paper we show that by using the more general concept of a frame the problem of existence of a frame based on the Szegö kernel has a solution.

Keywords: Duffin–Schaeffer frames, Banach frames, framing model, reproducing kernel Hilbert space, Hardy space, Szegö kernel.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00414_а


DOI: https://doi.org/10.26907/0021-3446-2019-2-57-68

Full text: PDF file (230 kB)
First page: PDF file
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UDC: 517.518
Received: 05.12.2017
Revised: 09.01.2018
Accepted: 22.03.2018

Citation: K. S. Speransky, P. A. Terekhin, “On existence of frames based on the Szegö kernel in the Hardy space”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 2, 57–68

Citation in format AMSBIB
\Bibitem{SpeTer19}
\by K.~S.~Speransky, P.~A.~Terekhin
\paper On existence of frames based on the Szeg\"{o} kernel in the Hardy space
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2019
\issue 2
\pages 57--68
\mathnet{http://mi.mathnet.ru/ivm9440}
\crossref{https://doi.org/10.26907/0021-3446-2019-2-57-68}


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