Democratic systems of translates

JOURNAL OF APPROXIMATION THEORY

卷:171

Article

Hernandez, E.¹  Nielsen, M.²  Sikic, H.³  Soria, F.¹ 

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

[2] Aalborg Univ, Dept Math Sci, DK-9220 Aalborg, Denmark

[3] Univ Zagreb, Dept Math, HR-10000 Zagreb, Croatia

关键词: Greedy bases;    Democracy condition;    Shift invariant system;    Norm concentration;   

DOI  :  10.1016/j.jat.2013.03.001

来源: Elsevier

【 摘 要 】

Democratic systems arise in the context of greedy approximations in Banach spaces. Systems of translates of a single function are the basis of shift invariant subspaces and are used in the construction of wavelets and Gabor systems. In this article, we study the democracy in L-2(R) of the system of integer translates of a single function psi epsilon L-2 (R). Necessary and sufficient criteria are given in terms of properties of psi. The problem of finding an (operative) necessary and sufficient condition is still unsolved. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free