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Sampling in quasi shift-invariant spaces and Gabor frames generated by ratios of exponential polynomials
Alexander Ulanovskii1, Ilya Zlotnikov2,3
1Department of Mathematics and Physics, University of Stavanger, 4036 Stavanger, Norway.
Abstract:
We introduce two families of generators (functions) that consist of entire and meromorphic functions enjoying a certain periodicity property and contain the classical Gaussian and hyperbolic secant generators. Sharp results are proved on the density of separated sets that provide non-uniform sampling for the shift-invariant and quasi shift-invariant spaces generated by elements of these families. As an application, new sharp results are obtained on the density of semi-regular lattices for the Gabor frames generated by elements from these families.
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