  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 ${M_{u(m)b}T_{u(n)a}g:m,n\in \mathbb
N_{0}}$ to be a frame for L^2(K). The conditions proposed are stated in terms
of the Fourier transforms of the Gabor system's generating functions.
