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

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

2011-11-20

arxiv.org/abs/1111.4660v1

Mathematics

Classical Analysis and ODEs

Accepted for publication in GAFA seminar notes

Scientific paper

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.

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