8 papers · 1 filter
Non-linear approximation by -greedy bases
Pablo M. Berná, David González
The theory of greedy-like bases started in 1999 when S. V. Konyagin and V. N. Temlyakov introduced in \cite{KT} the famous Thresholding Greedy Algorithm. Since this year, different…
Extensions of democracy-like properties for sequences with gaps
Miguel Berasategui, Pablo M. Berná
In \cite{O2015}, T. Oikhberg introduced and studied variants of the greedy and weak greedy algorithms for sequences with gaps. In this paper, we extend some of the notions that app…
A functional characterization of almost greedy and partially greedy bases
Pablo M. Berná, Diego Mondéjar
In 2003, S. J. Dilworth et al. ([8]) introduced the notion of almost-greedy (resp. partially-greedy) bases. These bases were characterized in terms of quasi-greediness and democrac…
A note on partially-greedy bases in quasi-Banach spaces
Pablo M. Berná
We continue with the study of greedy-type bases in quasi-Banach spaces started in [3]. In this paper, we study partially-greedy bases focusing our attention in two main results: -C…
A remark on approximation with polynomials and greedy bases
Pablo M. Berná, Antonio Pérez
We investigate properties of the -th error of approximation by polynomials with constant coefficients and with modulus-constant coefficients $\mathcal{D}_{m…
Characterization of weight-semi-greedy bases
Pablo M. Berná
One classical result in greedy approximation theory is that almost-greedy and semi-greedy bases are equivalent in the context of Schauder bases in Banach spaces with finite cotype.…