A Family of Unitary Operators Satisfying a Poisson-type Summation Formula
Classical Analysis and ODEs
2011-11-22 v1 Functional Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.1111.4660,
title = {A Family of Unitary Operators Satisfying a Poisson-type Summation Formula},
author = {Dmitry Faifman},
journal= {arXiv preprint arXiv:1111.4660},
year = {2011}
}
Comments
Accepted for publication in GAFA seminar notes