Title

Affine frame decompositions and shift-invariant spaces

Authors

Authors

C. K. Chui;Q. Y. Sun

Comments

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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

WOS:000235687200005

ISSN

1063-5203

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