Frames for compactly supported functions with irrational density
Abstract
We find sufficient conditions on a compactly supported function g, g = [a,b] which guarantee that the Gabor system G(g;α,β)=\e2π i β m xg(x-α n)\m,n∈Z is a frame for all α < b-a, αβ < 1, αβ . These conditions are on one hand satisfied by almost all such functions, and on the other hand are explicit enough that we can give many concrete examples of the functions g which give us a frame e.g. g(x) = (1x4-1)(-1,1)(x).
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