Wavelet frames for (not necessarily reducing) affine subspaces

    Authors

    Q. Gu;D. G. Han

    Comments

    Authors: contact us about adding a copy of your work at STARS@ucf.edu

    Abbreviated Journal Title

    Appl. Comput. Harmon. Anal.

    Keywords

    Frames; Affine subspaces; Wavelet frames; Reducing subspaces; Mathematics, Applied; Physics, Mathematical

    Abstract

    An affine subspace is a closed linear subspace of L(2)(R) generated by an affine system {2(n/2)psi (2(n) t - l) | psi is an element of phi, n, l is an element of Z} for some subset phi subset of L(2)(R). Among affine subspaces. those that are reducing with respect to translation and dilation operators are well understood. The existence of singly generated wavelet frames for each reducing subspace has long been established, yet most affine subspaces are not reducing. This naturally leads to the question of whether every affine subspace admits a singly generated Parseval wavelet frame. We show that if an affine subspace is singly generated (i.e., if phi = {psi}), then it admits a Parseval wavelet frame with at most two generators. We provide some sufficient conditions under which a singly generated affine subspace admits a singly generated Parseval wavelet frame. In particular, this is true whenever (psi) over cap = chi(E) and {2(n/2)psi (2(n) t - l) | n, l is an element of Z} is a Bessel sequence. (C) 2008 Elsevier Inc. All rights reserved.

    Journal Title

    Applied and Computational Harmonic Analysis

    Volume

    27

    Issue/Number

    1

    Publication Date

    1-1-2009

    Document Type

    Article

    Language

    English

    First Page

    47

    Last Page

    54

    WOS Identifier

    WOS:000266570500004

    ISSN

    1063-5203

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