Title

Wavelet frames for (not necessarily reducing) affine subspaces

Authors

Authors

Q. Gu;D. G. Han

Comments

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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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