The WCGA in Lp(logL)a spaces

Garrigós Aniorte, Gustavo Adolfo

Publication:
The WCGA in Lp(logL)a spaces

dc.contributor.author	Garrigós Aniorte, Gustavo Adolfo
dc.contributor.department	Matemáticas
dc.date.accessioned	2026-01-25T09:23:32Z
dc.date.available	2026-01-25T09:23:32Z
dc.date.copyright	© 2023, The Author(s)
dc.date.created	2022
dc.date.issued	2023
dc.description.abstract	We present new results concerning Lebesgue-type inequalities for the Weak Chebyshev Greedy Algorithm (WCGA) in uniformly smooth Banach spaces X. First, we generalize a result of Temlyakov to cover situations in which the modulus of smoothness and the so called A3 parameter are not necessarily power functions. Secondly, we apply this new theorem to the Zygmund spaces Lp(log L)a , with 1<p<infty and a real, and show that, when the Haar system is used, then optimal recovery of N-sparse signals occurs for a suitable number Phi(N) of iterations, which is sharp when p\leq 2. Finally, an expression for Phi(N) in the case of the trigonometric system is also given.
dc.format	application/pdf
dc.format.extent	29
dc.identifier.citation	Constr Approx 61, 115–147 (2025).
dc.identifier.doi	https://doi.org/10.1007/s00365-023-09664-y
dc.identifier.eissn	1432-0940
dc.identifier.issn	0176-4276
dc.identifier.uri	http://hdl.handle.net/10201/193210
dc.language	eng
dc.publisher	Springer
dc.relation	Research partially supported by Grant PID2019-105599GB-I00 from Ministerio de Ciencia e Innovación (Spain), and Grants 20906/PI/18 and 21955/PI/22 from Fundación Séneca (Región de Murcia, Spain)
dc.relation.publisherversion	https://doi.org/10.1007/s00365-023-09664-y
dc.relation.replaces	https://arxiv.org/abs/2209.05404
dc.rights	Attribution-NonCommercial-NoDerivatives 4.0 International	*
dc.rights.accessRights	info:eu-repo/semantics/openAccess
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/4.0/	*
dc.subject	Non linear approximation
dc.subject	Greedy algorithm
dc.subject	Uniformly smooth Banach space
dc.subject	Orlicz space
dc.subject	Haar system
dc.subject	Trigonometric system
dc.subject.ods	No relacionado con ningún objetivo de desarrollo sostenible
dc.title	The WCGA in Lp(logL)a spaces
dc.type	info:eu-repo/semantics/article
dc.type.version	info:eu-repo/semantics/acceptedVersion
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