Journalartikel

Jahr der Veröffentlichung: 2006

Seiten: 108-125

Zeitschrift: Applied and Computational Harmonic Analysis

Bandnummer: 20

Heftnummer: 1

ISSN: 1063-5203

Open Access Status: Bronze

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

Verlag: 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-Zitierstil: 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-Zitierstil: 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