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Title: Uncertainty principle for Gabor systems and the Zak transform

Abstract

We show that if g(set-membership sign)L{sup 2}(R) is a generator of a Gabor orthonormal basis with the lattice ZxZ, then its Zak transform Z(g) satisfies {nabla}Z(g)(negated-set-membership sign)L{sup 2}([0,1){sup 2}). This is a generalization and extension of the Balian-Low uncertainty principle.

Authors:
;  [1]
  1. Institute of Mathematics, University of Wrodaw, Plac Grunwaldzki 2/4, 50-384 Wrodaw (Poland)
Publication Date:
OSTI Identifier:
20861566
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 47; Journal Issue: 12; Other Information: DOI: 10.1063/1.2393146; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; FOURIER TRANSFORMATION; LATTICE FIELD THEORY; MATHEMATICAL LOGIC; SET THEORY; UNCERTAINTY PRINCIPLE

Citation Formats

Czaja, Wojciech, and Zienkiewicz, Jacek. Uncertainty principle for Gabor systems and the Zak transform. United States: N. p., 2006. Web. doi:10.1063/1.2393146.
Czaja, Wojciech, & Zienkiewicz, Jacek. Uncertainty principle for Gabor systems and the Zak transform. United States. doi:10.1063/1.2393146.
Czaja, Wojciech, and Zienkiewicz, Jacek. Fri . "Uncertainty principle for Gabor systems and the Zak transform". United States. doi:10.1063/1.2393146.
@article{osti_20861566,
title = {Uncertainty principle for Gabor systems and the Zak transform},
author = {Czaja, Wojciech and Zienkiewicz, Jacek},
abstractNote = {We show that if g(set-membership sign)L{sup 2}(R) is a generator of a Gabor orthonormal basis with the lattice ZxZ, then its Zak transform Z(g) satisfies {nabla}Z(g)(negated-set-membership sign)L{sup 2}([0,1){sup 2}). This is a generalization and extension of the Balian-Low uncertainty principle.},
doi = {10.1063/1.2393146},
journal = {Journal of Mathematical Physics},
number = 12,
volume = 47,
place = {United States},
year = {Fri Dec 15 00:00:00 EST 2006},
month = {Fri Dec 15 00:00:00 EST 2006}
}