Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Speransky K. S. On the convergence of the order-preserving weak greedy algorithm for subspaces generated by the Szego kernel in the Hardy space. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2021, vol. 21, iss. 3, pp. 336-342. DOI: 10.18500/1816-9791-2021-21-3-336-342, EDN: XUZAEH

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
31.08.2021
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English
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517.5
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XUZAEH

On the convergence of the order-preserving weak greedy algorithm for subspaces generated by the Szego kernel in the Hardy space

Autors: 
Speransky Konstantin Sergeevich, Saratov State University
Abstract: 

In this article we consider representing properties of subspaces generated by the Szego kernel. We examine under which conditions on the sequence of points of the unit disk the order-preserving weak greedy algorithm for appropriate subspaces generated by the Szego kernel converges. Previously, we constructed a representing system based on discretized Szego kernels. The aim of this paper is to find an effective algorithm to get such representation, and we draw on the work of Silnichenko that introduced the notion of the order-preserving weak greedy algorithm. By selecting a special sequence of discretization points we refine one of Totik's results on the approximation of functions in the Hardy space using Szego kernels. As the main result we prove the convergence criteria of the order-preserving weak greedy algorithm for subspaces generated by the Szego kernel in the Hardy space.

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Received: 
10.11.2020
Accepted: 
04.12.2020
Published: 
31.08.2021