Lebesgue-type inequalities in greedy approximation

S. Dilworth; G. Garrigós; E. Hernández; D. Kutzarova; V. Temlyakov

doi:10.1016/j.jfa.2020.108885

Lebesgue-type inequalities in greedy approximation

S. Dilworth, G. Garrigós, E. Hernández, D. Kutzarova, V. Temlyakov

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We present new results regarding Lebesgue-type inequalities for the Weak Chebyshev Greedy Algorithm (WCGA) in uniformly smooth Banach spaces. We improve earlier bounds in [19] for dictionaries satisfying a new property introduced here. We apply these results to derive optimal bounds in two natural examples of sequence spaces. In particular, optimality is obtained in the case of the multivariate Haar system in L^p with 1<p≤2, under the Littlewood-Paley norm.

Original language	English (US)
Article number	108885
Journal	Journal of Functional Analysis
Volume	280
Issue number	5
DOIs	https://doi.org/10.1016/j.jfa.2020.108885
State	Published - Mar 1 2021

Keywords

Non-linear approximation
Thresholding greedy algorithm
Uniformly smooth Banach space
Weak Chebyshev greedy algorithm

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2020.108885

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title = "Lebesgue-type inequalities in greedy approximation",

abstract = "We present new results regarding Lebesgue-type inequalities for the Weak Chebyshev Greedy Algorithm (WCGA) in uniformly smooth Banach spaces. We improve earlier bounds in [19] for dictionaries satisfying a new property introduced here. We apply these results to derive optimal bounds in two natural examples of sequence spaces. In particular, optimality is obtained in the case of the multivariate Haar system in Lp with 1",

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AU - Kutzarova, D.

AU - Temlyakov, V.

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KW - Non-linear approximation

KW - Thresholding greedy algorithm

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Lebesgue-type inequalities in greedy approximation

Abstract

Keywords

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