2011/11/20 by Dmitry Faifman, Faifman, Dmitry
Engineering · Mathematics · #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Material Science and Thermodynamics #math.CA #math.FA
paper · pdf · doi:10.48550/arxiv.1111.4660
Accepted for publication in GAFA seminar notes
arxiv created 2011/11/20 · openalex publication_date 2011/11/20 · arxiv updated 2011/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.