Abstract
In this article we study Gabor systems for non-rectangular lattices. We construct a modified Zak-transform which diagonalizes the Gabor frame operator corresponding to non-rectangular lattices at critical density. We also construct a representation of the Gabor frame operator similar to the Walnut representation. The key tool to develop these results is the fractional Fourier-transform. This approach for studying Gabor systems for non-rectangular lattices is to some extent complementary to the conventional method based on the representation theory on the Heisenberg-group.
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