Affine frame decompositions and shift-invariant spaces

    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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