Extensions of Bessel sequences to dual pairs of frames

Title
Extensions of Bessel sequences to dual pairs of frames
Author(s)
김래영Ole Christensen[Ole Christensen]김홍오[김홍오]
Keywords
AFFINE SYSTEMS; L-2(R-D)
Issue Date
201303
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Citation
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, v.34, no.2, pp.224 - 233
Abstract
Tight frames in Hilbert spaces have been studied intensively for the past years. In this paper we demonstrate that it often is an advantage to use pairs of dual frames rather than tight frames. We show that in any separable Hilbert space, any pairs of Bessel sequences can be extended to a pair of dual frames. If the given Bessel sequences are Gabor systems in L-2(R), the extension can be chosen to have Gabor structure as well. We also show that if the generators of the given Gabor Bessel sequences are compactly supported, we can choose the generators of the added Gabor systems to be compactly supported as well. This is a significant improvement compared to the extension of a Bessel sequence to a tight frame, where the added generator only can be compactly supported in some special cases. We also analyze the wavelet case, and find sufficient conditions under which a pair of wavelet systems can be extended to a pair of dual frames. (C) 2012 Elsevier Inc. All rights reserved.
URI
http://hdl.handle.net/YU.REPOSITORY/26213http://dx.doi.org/10.1016/j.acha.2012.04.003
ISSN
1063-5203
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이과대학 > 수학과 > Articles
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