Poisson summation formulae and the wave equation with a finitely supported measure as initial velocity
type: Item
instance of: scholarly article
title: Poisson summation formulae and the wave equation with a finitely supported measure as initial velocity
zbMATH Open document ID: 1377.42010
author: Yves Meyer
author: J. I. Díaz
published in: African Diaspora Journal of Mathematics
publication date: 2017-07-28T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.adjm/1495072816
review text: Besides new Poisson summation formulae recently discovered by Lev and Olevskii, there are some other examples in an old paper by \textit{A. P. Guinand} [Acta Math. 101, 235--271 (1959; Zbl 0085.30102)]. Guinand's work follows from some simple observations on solutions of the wave equation on the three-dimensional torus. If the initial velocity is a Dirac mass at the origin, the solution is Guinand's distribution. By a new approach suggested in the paper under review, one can construct a large family of initial velocities which give rise to crystalline measures generalizing Guinand's solution.
reviewed by: Elijah Liflyand
Mathematics Subject Classification ID: 42A75
Mathematics Subject Classification ID: 28A12
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 6754626
zbMATH Keywords: wave equation
zbMATH Keywords: Poisson summation formula
zbMATH Keywords: crystalline measure
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6754626