Gabor frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of engineering and science. Finding general and verifiable conditions which imply that the Gabor systems are Gabor frames is among the core problems in time-frequency analysis. In this paper, we give some simple and sufficient conditions that ensure a Gabor system {M_u(m)bT_u(n)ag =: χ_m(bx)g (x-u(n)a)}_{m,n∊ ℕ0} to be a frame for L²(K). The conditions proposed are stated in terms of the Fourier transforms of the Gabor system's generating functions.

Tbilisi Mathematical Journal, Vol. 9(2) (2016), pp. 129-139