Density of Gabor Systems Via the Short Time Fourier Transform
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Author(s)
Clark, William
Nitzan, Shahaf
Sullivan, Joseph
Ahn, Andrew Jeehyun
Date Issued
March 2017
Journal
Journal of Fourier Analysis and Applications
Publisher
Springer US
Citation
Ahn, Andrew, et al. “Density of Gabor Systems Via the Short Time Fourier Transform.” Journal of Fourier Analysis and Applications, vol. 24, no. 3, June 2018, pp. 699–718.
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Brain and Cognitive Sciences
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00041-017-9535-9
