Gabor Schauder bases and the Balian-Low theorem

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Weight Functions in Time-Frequency Analysis (2006, background): “A first and fascinating application of Muckenhaupt weights in time-frequency analysis was found by Heil and Powell [25] in their investigation of Gabor systems at the critical density.”
Weight Functions in Time-Frequency Analysis (2006, background): “ime-frequency shifts and thus do not fall under the realm of time-frequency analysis. A ﬁrst and fascinating application of Muckenhaupt weights in time-frequency analysis was found by Heil and Powell [25] in their investigation of Gabor systems at the critical density. They proved that the Gabor sys”