New parameters and Lebesgue-type estimates in greedy approximation
The purpose of this paper is to quantify the size of the Lebesgue constants $(\boldsymbol {L}_m)_{m=1}^{\infty }$ 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 allo...
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| Veröffentlicht in: | Forum of Mathematics, Sigma Jg. 10 |
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| Hauptverfasser: | , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge, UK
Cambridge University Press
01.01.2022
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| Schlagworte: | |
| ISSN: | 2050-5094, 2050-5094 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | The purpose of this paper is to quantify the size of the Lebesgue constants
$(\boldsymbol {L}_m)_{m=1}^{\infty }$
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
$(\boldsymbol {k}_m)_{m=1}^{\infty }$
determines the growth of
$(\boldsymbol {L}_m)_{m=1}^{\infty }$
. Multiple theoretical applications and computational examples complement our study. |
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| Bibliographie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 2050-5094 2050-5094 |
| DOI: | 10.1017/fms.2022.102 |