Geodesic
New parameters and Lebesgue-type estimates in greedy approximation
Forum of Mathematics, Sigma, Tome 10 (2022)

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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. 
@article{10_1017_fms_2022_102,
     author = {Fernando Albiac and Jos\'e L. Ansorena and Pablo M. Bern\'a},
     title = {New parameters and {Lebesgue-type} estimates in greedy approximation},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {10},
     year = {2022},
     doi = {10.1017/fms.2022.102},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.102/}
}
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Fernando Albiac; José L. Ansorena; Pablo M. Berná. New parameters and Lebesgue-type estimates in greedy approximation. Forum of Mathematics, Sigma, Tome 10 (2022). doi: 10.1017/fms.2022.102

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