Revista Matemática Iberoamericana

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Volume 33, Issue 3, 2017, pp. 1025–1036
DOI: 10.4171/RMI/962

Measures with locally finite support and spectrum

Yves Meyer[1]

(1) ENS Cachan, France

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].

Keywords: Quasicrystals, Poisson summation formula

Meyer Yves: Measures with locally finite support and spectrum. Rev. Mat. Iberoamericana 33 (2017), 1025-1036. doi: 10.4171/RMI/962