Abstract:We give a full description of complete interpolating sequences for the shiftinvariant space generated by the Gaussian. As a consequence, we rederive the known density conditions for sampling and interpolation.
Main resultsConsider the shift-invariant space of functions on R with Gaussian generator g(z) = e −az 2 for a > 0 defined asWe consider the space V 2 as a subspace of L 2 (R) with the usual L 2 -norm.The space V 2 belongs to the general family of shift-invariant spaces. Given a generator g ∈ L 2 (R), suc… Show more
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