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Density of Gabor Systems Via the Short Time Fourier Transform |
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| Authors: | Andrew?Ahn William?Clark |
| Institution: | 1.School of Mathematical Sciences,Massachusetts Institute of Technology,Cambridge,USA;2.Department of Mathematics,University of Michigan,Ann Arbor,USA;3.School of Mathematical Sciences,Georgia Institute of Technology,Atlanta,USA;4.Department of Physics,Yale University,New Haven,USA |
| 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. |
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