Riesz bases in L2(0,1) related to sampling in shift-invariant spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:308

Article

García, AG ; Pérez-Villalón, G ; Portal, A

关键词: shift-invariant spaces;    Zak transform;    Riesz bases;    sampling expansions;   

DOI  :  10.1016/j.jmaa.2004.11.058

来源: Elsevier

【 摘 要 】

The Fourier duality is an elegant technique to obtain sampling formulas in Paley-Wiener spaces. In this paper it is proved that there exists an analogue of the Fourier duality technique in the setting of shift-invariant spaces. In fact, any shift-invariant space V. with a stable generator phi is the range space of a bounded one-to-one linear operator T between L-2(0, 1) and L2(R). Thus, regular and irregular sampling formulas in V,, are obtained by transforming, via T, expansions in L2 (0, 1) with respect to some appropriate Riesz bases, (c) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

Free