Frame properties of generalized shift-invariant systems in discrete setting. Issue 11 (1st November 2016)

• Record Type: Journal Article
• Authors: Lu, Dayong; Li, Dengfeng
• Is Part Of: Applicable analysis. Volume 95:Issue 11(2016)
• Page Start: 2535
• Page End: 2552
• Publication Date: 2016-11-01
• Subjects: Frame -- shift-invariant system -- affine system -- Gabor system -- wavelet -- Calderón condition; 42C15 -- 42C40; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2015.1096347
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper, we present a simple characterization of those sequences for which purely shift-invariant systems are normalized tight frames for . As an application, a characterization for the Gabor system to be a normalized tight frame can be directly derived. Further, we prove that if the Calderón condition holds, then such purely shift-invariant systems are still normalized tight frames for . At the end of the paper, a sufficient condition for those purely shift-invariant systems to be frames for is established which is a variant of the classical wavelet systems to be frames for .