Basic Results of Gabor Frame on Local Fields*

Abstract

Basic facts for Gabor frame {E _u(m)b T _u(n)a g} _{m, n}∈ρ on local field are investigated. Accurately, that the canonical dual of frame {E _u(m)b T _u(n)a g} _{m, n}∈ρ also has the Gabor structure is showed; that the product ab decides whether it is possible for {E _u(m)b T _u(n)a g} _{m, n}∈ρ to be a frame for L ²(K) is discussed; some necessary conditions and two sufficient conditions of Gabor frame for L ²(K) are established. An example is finally given.

Keywords

Frame / Gabor frame / Local field / 42C15 / 42C40

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