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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| Vydáno v: | Forum of Mathematics, Sigma Ročník 10 |
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Cambridge University Press
01.01.2022
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| Abstract | 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. |
|---|---|
| AbstractList | 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. 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. 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. |
| ArticleNumber | e113 |
| Author | Ansorena, José L. Albiac, Fernando Berná, Pablo M. |
| Author_xml | – sequence: 1 givenname: Fernando orcidid: 0000-0001-7051-9279 surname: Albiac fullname: Albiac, Fernando email: fernando.albiac@unavarra.es organization: 1Department of Mathematics, Statitistics, and Computer Sciences–InaMat2, Universidad Pública de Navarra, Campus de Arrosadía, 31006, Spain; E-mail: fernando.albiac@unavarra.es – sequence: 2 givenname: José L. orcidid: 0000-0002-4979-1080 surname: Ansorena fullname: Ansorena, José L. email: joseluis.ansorena@unirioja.es organization: 2Department of Mathematics and Computer Sciences, Universidad de La Rioja, Logroño, 26004, Spain; E-mail: joseluis.ansorena@unirioja.es – sequence: 3 givenname: Pablo M. orcidid: 0000-0001-7685-0886 surname: Berná fullname: Berná, Pablo M. email: pablo.berna@cunef.edu organization: 3Departamento de Métodos Cuantitativos, CUNEF Universidad, Madrid, 28040, Spain; E-mail: pablo.berna@cunef.edu |
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| Cites_doi | 10.1016/j.jat.2014.09.001 10.4171/rmi/1062 10.1007/s00365-002-0525-y 10.1007/s00365-015-9293-3 10.4064/sm211-1-3 10.1006/acha.1993.1008 10.1016/j.jat.2005.09.017 10.1090/cbms/079 10.2307/2007000 10.2989/16073606.2017.1393704 10.1007/s00365-018-9415-9 10.1007/s13163-016-0204-3 10.1007/s13163-017-0221-x 10.1016/j.jat.2011.02.013 10.1007/BF02514500 10.1007/s00365-019-09466-1 10.1006/jath.2000.3512 10.1007/s003659900090 10.1016/0022-1236(90)90137-A 10.1353/ajm.1999.0016 10.1112/S0024611503014084 10.1215/S0012-7094-49-01619-1 10.1007/s00365-013-9209-z 10.4064/sm159-1-4 10.1016/j.jmaa.2014.09.018 10.1016/j.jfa.2018.08.015 10.1006/jath.2001.3641 10.1090/S0002-9939-1959-0116184-5 10.7169/facm/2014.50.2.1 10.1023/A:1018900431309 10.1007/s00208-020-02069-3 10.1007/s10444-010-9155-2 10.1007/BF02414186 10.1016/j.jat.2018.03.002 10.1016/0021-9045(90)90005-B 10.1007/BF02390514 |
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| Snippet | 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... 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... |
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| SubjectTerms | Analysis Approximation Banach spaces Democracy Estimates Greedy algorithms Parameters Symmetry |
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| Title | New parameters and Lebesgue-type estimates in greedy approximation |
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