Density of Gabor Systems Via the Short Time Fourier Transform

We apply a new approach to the study of the density of Gabor systems, and obtain a simple and straightforward proof to Ramanathan and Steger’s well-known result regarding the density of Gabor frames and Gabor Riesz sequences. Moreover, this point of view allows us to extend this result in several di...

Full description

Bibliographic Details
Main Authors: Clark, William, Nitzan, Shahaf, Sullivan, Joseph, Ahn, Andrew Jeehyun
Other Authors: Massachusetts Institute of Technology. Department of Brain and Cognitive Sciences
Format: Article
Language:English
Published: Springer US 2018
Online Access:http://hdl.handle.net/1721.1/116407
https://orcid.org/0000-0001-6413-1411
Description
Summary:We apply a new approach to the study of the density of Gabor systems, and obtain a simple and straightforward proof to Ramanathan and Steger’s well-known result regarding the density of Gabor frames and Gabor Riesz sequences. Moreover, this point of view allows us to extend this result in several directions. The approach we use was first observed by Olevskii and the third author in their study of exponential systems, here we develop and simplify it further.