Approximation by polynomials with constant coefficients and the Thresholding Greedy Algorithm

Name: Approximation by polynomials with constant coefficients and the Thresholding Greedy Algorithm
Keywords: Mathematics - Functional Analysis, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), unconditional bases, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, FOS: Mathematics, greedy bases, Functional Analysis (math.FA), 46B15

Berasategui, Miguel; Berná, Pablo M.; González, David

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Preprint . 2023

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zbMATH Open

Article . 2025

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Carpathian Journal of Mathematics

Article . 2024 . Peer-reviewed

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https://dx.doi.org/10.48550/ar...

Article . 2023

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Approximation by polynomials with constant coefficients and the Thresholding Greedy Algorithm

Approximation by polynomials with constant coefficients and the thresholding greedy algorithm

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 10 Apr 2024Embargo end date: 01 Jan 2023Publisher:Technical University of Cluj Napoca, North University Center of Baia MareJournal:Carpathian Journal of Mathematics, volume 41, pages 31-44 (issn: 1584-2851, eissn: 1843-4401,

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Authors: Berasategui, Miguel; Berná, Pablo M.; González, David;

doi: 10.37193/cjm.2025.01.03 , 10.48550/arxiv.2309.14607

arXiv: 2309.14607

Approximation by polynomials with constant coefficients and the Thresholding Greedy Algorithm

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Abstract

Greedy bases are those bases where the Thresholding Greedy Algorithm (introduced by S. V. Konyagin and V. N. Temlyakov) produces the best possible approximation up to a constant. In 2017, P. M. Bern´a and ´O. Blasco gave a characterization of these bases using polynomials with constant coefficients. In this paper, we continue this study improving some optimization problems and extending some results to the context of quasi-Banach spaces.

Keywords

Mathematics - Functional Analysis, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), unconditional bases, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, FOS: Mathematics, greedy bases, Functional Analysis (math.FA), 46B15

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