Poisson summation formulae and the wave equation with a finitely supported measure as initial velocity (Q2012160)

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.