A remark on approximation with polynomials and greedy bases

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:478

Article

Berna, Pablo M.¹  Perez, Antonio² 

[1] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

[2] UCM, UC3M, UAM, Inst Ciencias Matemat,CSIC, C Nicolas Cabrera 13-15,Campus Cantoblanco, Madrid 28049, Spain

关键词: Thresholding greedy algorithm;    Greedy bases;    Almost greedy bases;   

DOI  :  10.1016/j.jmaa.2019.05.038

来源: Elsevier

【 摘 要 】

We investigate properties of the m-th error of approximation by polynomials with constant coefficients 9,,(x) and with modulus-constant coefficients D-m(x) introduced by Bernd and Blasco (D-m* (x) to study greedy bases in Banach spaces. We characterize when lim inf (x) and lim inf n D-m(x) are equivalent to parallel to x parallel to in terms of the democracy and superdemocracy functions, and provide sufficient conditions ensuring that D-m*9,(x) = extending previous very particular results. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free