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. © 2012 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Faifman, D. (2012). A family of unitary operators satisfying a poisson-type summation formula. Lecture Notes in Mathematics, 2050, 191–204. https://doi.org/10.1007/978-3-642-29849-3_11
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