Journal article

Publication year: 2006

Pages: 108-125

Journal: Applied and Computational Harmonic Analysis

Volume number: 20

Issue number: 1

ISSN: 1063-5203

Open access status: Bronze

DOI Link: https://doi.org/10.1016/j.acha.2005.04.002

Publisher: Elsevier

Abstract: 
We study wave packet systems WP(psi, M); that is, countable collections of dilations, translations, and modulations of a single function psi is an element of L-2(R). The parameters of these unitary actions form a discrete subset M subset of R+ x R x R. We introduce analogues of the notion of Beurling density, adapted to the geometry of discrete subsets of R+ x R x R, and notions of lower and upper dimensions associated with these densities. Our goal is to describe completeness properties of wave packet systems via geometric properties of the sets of their parameters. In particular, we show necessary conditions for WP (psi, M) to be a Bessel system, and we construct multiple examples of non-standard wave packet frames with prescribed dimensions. (C) 2005 Elsevier Inc. All rights reserved.

Harvard Citation style: Czaja, W., Kutyniok, G. and Speegle, D. (2006) The geometry of sets of parameters of wave packet frames, Applied and Computational Harmonic Analysis, 20(1), pp. 108-125. https://doi.org/10.1016/j.acha.2005.04.002

APA Citation style: Czaja, W., Kutyniok, G., & Speegle, D. (2006). The geometry of sets of parameters of wave packet frames. Applied and Computational Harmonic Analysis. 20(1), 108-125. https://doi.org/10.1016/j.acha.2005.04.002