Twenty-five years of greedy bases
| dc.contributor.author | Albiac Alesanco, Fernando José | |
| dc.contributor.author | Ansorena, José L. | |
| dc.contributor.author | Temlyakov, Vladimir | |
| dc.contributor.department | Estadística, Informática y Matemáticas | es_ES |
| dc.contributor.department | Estatistika, Informatika eta Matematika | eu |
| dc.contributor.department | Institute for Advanced Materials and Mathematics - INAMAT2 | en |
| dc.date.accessioned | 2025-03-03T12:45:12Z | |
| dc.date.issued | 2025-05-01 | |
| dc.date.updated | 2025-03-03T12:23:06Z | |
| dc.description.abstract | Although the basic idea behind the concept of a greedy basis had been around for some time, the formal development of a theory of greedy bases was initiated in 1999 with the publication of the article [S.V. Konyagin and V.N. Temlyakov, A remark on greedy approximation in Banach spaces, East J. Approx. 5 (3) (1999), 365-379]. The theoretical simplicity of the thresholding greedy algorithm became a model for a procedure widely used in numerical applications and the subject of greedy bases evolved very rapidly from the point of view of approximation theory. The idea of studying greedy bases and related greedy algorithms attracted also the attention of researchers with a classical Banach space theory background. From the more abstract point of functional analysis, the theory of greedy bases and its derivates evolved very fast as many fundamental results were discovered and new ramifications branched out. Hundreds of papers on greedy-like bases and several monographs have been written since the appearance of the aforementioned foundational paper. After twenty-five years, the theory is very much alive and it continues to be a very active research topic both for functional analysts and for researchers interested in the applied nature of nonlinear approximation alike. This is why we believe it is a good moment to gather a selection of 25 open problems (one per year since 1999!) whose solution would contribute to advance the state of art of this beautiful topic. | en |
| dc.description.sponsorship | The research of F. Albiac and J.L. Ansorena was partially funded by the Spanish Ministry for Science and Innovation under Grant PID2022-138342NB-I00 for Functional analysis methods in approximation theory and applications. The research of V.N. Temlyakov (Section 13) was supported by the Russian Science Foundation under Grant No. 23-71-30001, https://rscf.ru/project/23-71-30001/, and performed at Lomonosov Moscow State University. | |
| dc.embargo.lift | 2027-05-01 | |
| dc.embargo.terms | 2027-05-01 | |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.citation | Albiac, F., Ansorena, J. L., Temlyakov, V. (2025) Twenty-five years of greedy bases. Journal of Approximation Theory, 307, 1-23. https://doi.org/10.1016/j.jat.2024.106141 | |
| dc.identifier.doi | 10.1016/j.jat.2024.106141 | |
| dc.identifier.issn | 0021-9045 | |
| dc.identifier.uri | https://academica-e.unavarra.es/handle/2454/53645 | |
| dc.language.iso | eng | |
| dc.publisher | Elsevier | |
| dc.relation.ispartof | Journal of Approximation Theory, 307(2025), 1-23 | |
| dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2022-138342NB-I00/ES/ | |
| dc.relation.publisherversion | https://doi.org/10.1016/j.jat.2024.106141 | |
| dc.rights | © 2024 Elsevier Inc. This manuscript version is made available under the CC-BY-NC-ND 4.0. | |
| dc.rights.accessRights | info:eu-repo/semantics/embargoedAccess | |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject | Almost greedy | en |
| dc.subject | And quasi-greedy basis | en |
| dc.subject | Greedy | en |
| dc.subject | Nonlinear approximation | en |
| dc.subject | Thresholding greedy algorithm | en |
| dc.title | Twenty-five years of greedy bases | en |
| dc.type | info:eu-repo/semantics/article | |
| dc.type.version | info:eu-repo/semantics/acceptedVersion | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 3a702006-6ba1-41ba-93bf-ea9fee1de239 | |
| relation.isAuthorOfPublication.latestForDiscovery | 3a702006-6ba1-41ba-93bf-ea9fee1de239 |