Please use this identifier to cite or link to this item: https://doi.org/10.1117/12.279692
Title: Characterizations of wavelet bases and frames in Hilbert spaces
Authors: Lee, S.L. 
Tang, W.S. 
Keywords: Bessel sequences
Frames
Riesz bases
Issue Date: 1997
Citation: Lee, S.L., Tang, W.S. (1997). Characterizations of wavelet bases and frames in Hilbert spaces. Proceedings of SPIE - The International Society for Optical Engineering 3169 : 282-290. ScholarBank@NUS Repository. https://doi.org/10.1117/12.279692
Abstract: Let U = (Ui,...,Ud) be an ordered d-tuple of distinct commuting unitary operators on a complex Hilbert space H, and Y = {y 1,...,ys}a finite subset of H. Let UZd (Y) = {Unyj : n ∈ Zd,j = 1,...,s}, and let Φ(θ) be the s by s matrix function (sequences presented) defined on the d-dimensional torus. We obtain characterizations, in terms of the matrix function Φ(θ), for the set Uzd (Y) to be (1) a Bessel sequence; or (2) a (tight) frame; or (3) a Riesz basis for its closed linear span in H. Connections with other related work will also be discussed.
Source Title: Proceedings of SPIE - The International Society for Optical Engineering
URI: http://scholarbank.nus.edu.sg/handle/10635/104542
ISSN: 0277786X
DOI: 10.1117/12.279692
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