Title
Affine Frame Decompositions And Shift-Invariant Spaces
Abstract
In this paper, we show that the property of tight affine frame decomposition of functions in L2 can be extended in a stable way to functions in Sobolev spaces when the generators of the tight affine frames satisfy certain mild regularity and vanishing moment conditions. Applying the affine frame operators Qj on jth levels to any function f in a Sobolev space reveals the detailed information Qjf of f in such tight affine decompositions. We also study certain basic properties of the range of the affine frame operators Qj such as the topological property of closedness and the notion of angles between the ranges for different levels, and thus establishing some interesting connection to (tight) frames of shift-invariant spaces. © 2005 Elsevier Inc. All rights reserved.
Publication Date
1-1-2006
Publication Title
Applied and Computational Harmonic Analysis
Volume
20
Issue
1
Number of Pages
74-107
Document Type
Article; Proceedings Paper
Personal Identifier
scopus
DOI Link
https://doi.org/10.1016/j.acha.2005.09.003
Copyright Status
Unknown
Socpus ID
32044469424 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/32044469424
STARS Citation
Chui, Charles K. and Sun, Qiyu, "Affine Frame Decompositions And Shift-Invariant Spaces" (2006). Scopus Export 2000s. 9158.
https://stars.library.ucf.edu/scopus2000/9158