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Lebesgue-type inequalities in greedy approximation

Publicated to:JOURNAL OF FUNCTIONAL ANALYSIS. 280 (5): - 2021-03-01 280(5), DOI: 10.1016/j.jfa.2020.108885

Authors: Dilworth S; Garrigós G; Hernández E; Kutzarova D; Temlyakov V

Affiliations

Institute of Mathematics and Informatics Bulgarian Academy of Sciences - Author
Lomonosov Moscow State University - Author
Moscow Center for Fundamental and Applied Mathematics - Author
Steklov Mathematical Institute of RAS - Author
Universidad Autónoma de Madrid - Author
Universidad de Murcia - Author
University of Illinois at Urbana-Champaign - Author
University of South Carolina - Author
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Abstract

© 2020 Elsevier Inc. 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

Keywords

Non-linear approximationThresholding greedy algorithmUniformly smooth banach spaceWeak chebyshev greedy algorithm

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal JOURNAL OF FUNCTIONAL ANALYSIS due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2021, it was in position 47/333, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics.

From a relative perspective, and based on the normalized impact indicator calculated from World Citations provided by WoS (ESI, Clarivate), it yields a value for the citation normalization relative to the expected citation rate of: 1.24. This indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: ESI Nov 14, 2024)

This information is reinforced by other indicators of the same type, which, although dynamic over time and dependent on the set of average global citations at the time of their calculation, consistently position the work at some point among the top 50% most cited in its field:

  • Weighted Average of Normalized Impact by the Scopus agency: 1.43 (source consulted: FECYT Feb 2024)
  • Field Citation Ratio (FCR) from Dimensions: 4.97 (source consulted: Dimensions Jun 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-06-27, the following number of citations:

  • WoS: 3
  • Scopus: 6

Impact and social visibility

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • The work has been submitted to a journal whose editorial policy allows open Open Access publication.

Leadership analysis of institutional authors

This work has been carried out with international collaboration, specifically with researchers from: Bulgaria; Russia; United States of America.