A family of unitary operators satisfying a poisson-type summation formula

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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.

Original languageEnglish
Title of host publicationGeometric Aspects of Functional Analysis
Subtitle of host publicationIsrael Seminar 2006-2010
PublisherSpringer Verlag
Pages191-204
Number of pages14
ISBN (Print)9783642298486
DOIs
StatePublished - 2012

Publication series

NameLecture Notes in Mathematics
Volume2050
ISSN (Print)0075-8434

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