Basic Results of Gabor Frame on Local Fields*

Basic facts for Gabor frame {Eu(m)bTu(n)ag}m, n∈ρ on local field are investigated. Accurately, that the canonical dual of frame {Eu(m)bTu(n)ag}m, n∈ρ also has the Gabor structure is showed; that the product ab decides whether it is possible for {Eu(m)bTu(n)ag}m, n∈ρ to be a frame for L2(K) is discussed; some necessary conditions and two sufficient conditions of Gabor frame for L2(K) are established. An example is finally given.