Lebesgue inequalities for Chebyshev thresholding greedy algorithms

Lebesgue inequalities for Chebyshev thresholding greedy algorithms

We establish estimates for the Lebesgue parameters of the Chebyshev weak thresholding greedy algorithm in the case of general bases in Banach spaces. These generalize and slightly improve earlier results in Dilworth et al. (Rev Mat Complut 28(2):393–409, 2015), and are complemented with examples sho...

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Veröffentlicht in:Revista matemática complutense 2020-09, Vol.33 (3), p.695-722
Hauptverfasser: Berná, P. M., Blasco, Ó., Garrigós, G., Hernández, E., Oikhberg, T.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Analysis
Applications of Mathematics
Banach spaces
Chebyshev approximation
Geometry
Greedy algorithms
Mathematics
Mathematics and Statistics
Parameter estimation
Topology
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Zusammenfassung:We establish estimates for the Lebesgue parameters of the Chebyshev weak thresholding greedy algorithm in the case of general bases in Banach spaces. These generalize and slightly improve earlier results in Dilworth et al. (Rev Mat Complut 28(2):393–409, 2015), and are complemented with examples showing the optimality of the bounds. Our results also clarify certain bounds recently announced in Shao and Ye (J Inequal Appl 2018(1):102, 2018), and answer some questions left open in that paper.
ISSN:1139-1138
1988-2807
DOI:10.1007/s13163-019-00328-9