New parameters and Lebesgue-type estimates in greedy approximation
Fecha
2022Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión publicada / Argitaratu den bertsioa
Identificador del proyecto
AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-107701GB-I00/ES/
AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095366-B-I00/ES/
AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-105599GB-I00/ES/
Impacto
|
10.1017/fms.2022.102
Resumen
The purpose of this paper is to quantify the size of the Lebesgue constants (𝑳𝑚)∞
𝑚=1 associated with the thresholding
greedy algorithm in terms of a new generation of parameters that modulate accurately some features of a general
basis. This fine tuning of constants allows us to provide an answer to the question raised by Temlyakov in 2011 to
find a natural sequence of greedy-type paramet ...
[++]
The purpose of this paper is to quantify the size of the Lebesgue constants (𝑳𝑚)∞
𝑚=1 associated with the thresholding
greedy algorithm in terms of a new generation of parameters that modulate accurately some features of a general
basis. This fine tuning of constants allows us to provide an answer to the question raised by Temlyakov in 2011 to
find a natural sequence of greedy-type parameters for arbitrary bases in Banach (or quasi-Banach) spaces which
combined linearly with the sequence of unconditionality parameters (𝒌𝑚)∞
𝑚=1 determines the growth of (𝑳𝑚)∞
𝑚=1.
Multiple theoretical applications and computational examples complement our study. [--]
Materias
Lebesgue constants,
Greedy approximation
Editor
Cambridge University Press
Publicado en
Forum of Mathematics, Sigma, (2022), 10, 1-39
Departamento
Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas /
Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila /
Universidad Pública de Navarra/Nafarroako Unibertsitate Publikoa. Institute for Advanced Materials and Mathematics - INAMAT2
Versión del editor
Entidades Financiadoras
F. Albiac acknowledges the support of the Spanish Ministry for Science and Innovation underGrant PID2019-107701GB-I00 for Operators, lattices, and structure of Banach spaces. F. Albiac and J. L. Ansorena acknowledge the support of the Spanish Ministry for Science, Innovation, and Universities under Grant PGC2018-095366-B-I00 for Análisis Vectorial, Multilineal y Aproximacion. P. M. Berna acknowledges the support of the Spanish Ministry for Science and Innovation under Grant PID2019-105599GB-I00 and the Grant 20906/PI/18 from Fundacion Seneca (Region de Murcia, Spain). Open Access funding provided by Universidad Publica de Navarra