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...
Uložené v:
| Vydané v: | Forum of Mathematics, Sigma Ročník 10 |
|---|---|
| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Cambridge, UK
Cambridge University Press
01.01.2022
|
| Predmet: | |
| ISSN: | 2050-5094, 2050-5094 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Shrnutí: | 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. |
|---|---|
| Bibliografia: | 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 |