Registered users receive a variety of benefits including the ability to customize email alerts, create favorite journals list, and save searches.
Please note that a Project Euclid web account does not automatically grant access to full-text content. An institutional or society member subscription is required to view non-Open Access content.
Contact firstname.lastname@example.org with any questions.
New Poisson summation formulae have been recently discovered by Nir Lev and Alexander Olevskii since 2013. But some other examples were concealed in an old paper by Andrew Guinand dating from 1959. This was observed by the second author in 2016. In the present contribution a third approach is proposed. 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. Using this new approach one can construct a large family of initial velocities which give rise to crystalline measures generalizing Guinand's solution.