New parameters and Lebesgue-type estimates in greedy approximation - Albiac, Fernando; Ansorena, José L.; Berná, Pablo M. (Forum of Mathematics, Sigma, 2022)
The purpose of this paper is to quantify the size of the Lebesgue constants $(\boldsymbol {L}_m)_{m=1}^{∞ }$ 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 $(\boldsymbol {k}_m)_{m=1}^{∞ }$ determines the growth of $(\boldsymbol {L}_m)_{m=1}^{∞ }$ . Multiple theoretical applications and computational examples complement our study.