NDLI: Dimension invariance of finite frames of translates and Gabor frames

Content Provider	Springer Nature Link
Author	Cahill, Jameson Li, Shidong
Copyright Year	2011
Abstract	A dimension invariance property for finite frames of translates and Gabor frames is discussed. Under appropriate support conditions among the frame and dual frame generating functions, we show that a pair of dual frames evaluated in a given space remains a valid dual set if they are naturally embedded in the underlying space of almost arbitrarily enlarged dimension. Consequently, the evaluation of duals in a very large dimensional space is now easily accessible by merely working in a space of some much smaller dimension. A number of uniform and non-uniform schemes are studied. To satisfy the support conditions, a method of finding valid alternate dual functions with small support via a known parametric dual frame formula is discussed. Oftentimes it is convenient to have truncated approximate duals that satisfy the support conditions. Stability studies of the dimension invariance principle via such approximate duals are also presented.
Ending Page	520
Page Count	16
Starting Page	505
File Format	PDF
ISSN	10197168
e-ISSN	15729044
Journal	Advances in Computational Mathematics
Issue Number	4
Volume Number	37
Language	English
Publisher	Springer US
Publisher Date	2011-12-03
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Frames Frame expansions Numeric Computing Frame representations Multi-Gabor expansions Theory of Computation Mathematics Dual frames Dimension invariance Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) Algebra Calculus of Variations and Optimal Control; Optimization General harmonic expansions, frames Operators belonging to operator ideals (nuclear, $p$ -summing, in the Schatten-von Neumann classes, etc.) Multi-variable vector space Gabor frames
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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