# 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:

- 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}

}

DOI: 10.1063/1.2393146

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