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Frame constants of Gabor frames near the critical density:

Borichev, A. ; Gröchenig, K. ; Lyubarskii, Yu.
Journal de Mathématiques Pures et Appliquées.  94 (2010)  2 - p. 170-182 , 2010
Link: https://doi.org/10.1016/j.matpur.2010.01.001