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...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer US
2018
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| Online Access: | http://hdl.handle.net/1721.1/116407 https://orcid.org/0000-0001-6413-1411 |
| _version_ | 1811087145867149312 |
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| author | Clark, William Nitzan, Shahaf Sullivan, Joseph Ahn, Andrew Jeehyun |
| author2 | Massachusetts Institute of Technology. Department of Brain and Cognitive Sciences |
| author_facet | Massachusetts Institute of Technology. Department of Brain and Cognitive Sciences Clark, William Nitzan, Shahaf Sullivan, Joseph Ahn, Andrew Jeehyun |
| author_sort | Clark, William |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T13:40:47Z |
| format | Article |
| id | mit-1721.1/116407 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:40:47Z |
| publishDate | 2018 |
| publisher | Springer US |
| record_format | dspace |
| spelling | mit-1721.1/1164072024-07-15T18:00:05Z Density of Gabor Systems Via the Short Time Fourier Transform Clark, William Nitzan, Shahaf Sullivan, Joseph Ahn, Andrew Jeehyun Massachusetts Institute of Technology. Department of Brain and Cognitive Sciences Ahn, Andrew Jeehyun 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. 2018-06-19T14:35:22Z 2018-06-19T14:35:22Z 2017-03 2018-05-15T04:28:13Z Article http://purl.org/eprint/type/JournalArticle 1069-5869 1531-5851 http://hdl.handle.net/1721.1/116407 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. https://orcid.org/0000-0001-6413-1411 en https://doi.org/10.1007/s00041-017-9535-9 Journal of Fourier Analysis and Applications 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. Springer Science+Business Media New York application/pdf Springer US Springer US |
| spellingShingle | Clark, William Nitzan, Shahaf Sullivan, Joseph Ahn, Andrew Jeehyun Density of Gabor Systems Via the Short Time Fourier Transform |
| title | Density of Gabor Systems Via the Short Time Fourier Transform |
| title_full | Density of Gabor Systems Via the Short Time Fourier Transform |
| title_fullStr | Density of Gabor Systems Via the Short Time Fourier Transform |
| title_full_unstemmed | Density of Gabor Systems Via the Short Time Fourier Transform |
| title_short | Density of Gabor Systems Via the Short Time Fourier Transform |
| title_sort | density of gabor systems via the short time fourier transform |
| url | http://hdl.handle.net/1721.1/116407 https://orcid.org/0000-0001-6413-1411 |
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