Measures with locally finite support and spectrum

Abstract

This note answers an issue raised by Nir Lev and Alexander Olevskii in [7]. In the conclusion of [7] Lev and Olevskii mentioned a new and fascinating Poisson summation formula suggested by André Paul Guinand in [4]. Lev and Olevskii wanted to know to what class of functions this formula applies. This will be answered below (Theorem 4.1). Another intriguing Poisson summation formula was elaborated in [10]. We show that it is coupled to the Epstein ζ function by a coupling discovered by Jean-Pierre Kahane and Szolem Mandelbrojt in [5].