Title
Affine frame decompositions and shift-invariant spaces
Abbreviated Journal Title
Appl. Comput. Harmon. Anal.
Keywords
COMPACTLY SUPPORTED TIGHT; MAXIMUM VANISHING MOMENTS; LINEAR; INDEPENDENCE; REFINABLE FUNCTIONS; ORTHONORMAL BASES; BESOV-SPACES; WAVELETS; EQUATIONS; OPERATOR; FILTERS; Mathematics, Applied; Physics, Mathematical
Abstract
In this paper, we show that the property of tight affine frame decomposition of functions in L-2 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 Q(j) on jth levels to any function f in a Sobolev space reveals the detailed information Q(j) f of f in such tight affine decompositions. We also study certain basic properties of the range of the affine frame operators Q(j) 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. (C) 2005 Elsevier Inc. All rights reserved.
Journal Title
Applied and Computational Harmonic Analysis
Volume
20
Issue/Number
1
Publication Date
1-1-2006
Document Type
Article
Language
English
First Page
74
Last Page
107
WOS Identifier
ISSN
1063-5203
Recommended Citation
"Affine frame decompositions and shift-invariant spaces" (2006). Faculty Bibliography 2000s. 6031.
https://stars.library.ucf.edu/facultybib2000/6031
Comments
Authors: contact us about adding a copy of your work at STARS@ucf.edu