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A Family of Unitary Operators Satisfying a Poisson-type Summation Formula

We consider a weighted form of the Poisson summation formula. We prove that under certain decay rate conditions on the weights, there exists a unique unitary Fourier-Poisson operator which satisfies this formula. We next find the diagonal form of this operator, and prove that under weaker conditions on the weights, a unique unitary operator still exists which satisfies a Poisson summation formula in operator form. We also generalize the interplay between the Fourier transform and derivative to those Fourier-Poisson operators.

preprint2011arXivOpen access
Dmitry Faifman
math.FAmath.CA
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Dmitry Faifman

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