English

New parameters and Lebesgue-type estimates in greedy approximation

Functional Analysis 2021-04-23 v1

Abstract

The purpose of this paper is to quantify the size of the Lebesgue constants (Lm)m=1(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 (km)m=1(k_m)_{m=1}^{\infty} determines the growth of (Lm)m=1(L_m)_{m=1}^{\infty}. Multiple theoretical applications and computational examples complement our study.

Keywords

Cite

@article{arxiv.2104.10912,
  title  = {New parameters and Lebesgue-type estimates in greedy approximation},
  author = {Fernando Albiac and Jose L. Ansorena and Pablo M. Berna},
  journal= {arXiv preprint arXiv:2104.10912},
  year   = {2021}
}
R2 v1 2026-06-24T01:25:22.716Z