Abstract
In the article we investigate irregular Gabor frames. It is shown that for any Schwartz function ψ the family of its time–frequency shifts constitutes a weighted Gabor frame if only the lattice of sampling time– frequnecy–values is dense enough. The proof uses classical analysis tool only and bases on the localization of the kernel of the Gabor transform, further, the method allows to find the density bound explicitly. A numerical example is presented.
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