ISSN:
1572-9044
Keywords:
affine frame
;
quasi-affine frame
;
dual
;
sesquilinear operator
;
translation invariance
;
42C15 (primary)
;
42B15
;
47N40 (secondary)
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The notion of quasi-affine frame was recently introduced by Ron and Shen [9] in order to achieve shift-invariance of the discrete wavelet transform. In this paper, we establish a duality-preservation theorem for quasi-affine frames. Furthermore, the preservation of frame bounds when changing an affine frame to a quasi-affine frame is shown to hold without the decay assumptions in [9]. Our consideration leads naturally to the study of certain sesquilinear operators which are defined by two affine systems. The translation-invariance of such operators is characterized in terms of certain intrinsic properties of the two affine systems.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1018975725857
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