Phase space distribution of Gabor expansions
Functional Analysis
2008-05-28 v1 Classical Analysis and ODEs
Abstract
We present an example of a complete and minimal Gabor system consisting of time-frequency shifts of a Gaussian, localized at the coordinate axes in the time-frequency plane (phase space). Asymptotically, the number of time-frequency shifts contained in a disk centered at the origin is only 2/pi times the number of points from the von Neumann lattice found in the same disk. Requiring a certain regular distribution in phase space, we show that our system has minimal density among all complete and minimal systems of time-frequency shifts of a Gaussian.
Cite
@article{arxiv.0805.4166,
title = {Phase space distribution of Gabor expansions},
author = {Gerard Ascensi and Yurii I. Lyubarskii and Kristian Seip},
journal= {arXiv preprint arXiv:0805.4166},
year = {2008}
}
Comments
9 pages, submitted to publication