Revista Matemática Iberoamericana
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Published online: 2017-10-02
Measures with locally finite support and spectrumYves Meyer (1) ENS Cachan, France
This note answers an issue raised by Nir Lev and Alexander Olevskii in . In the conclusion of  Lev and Olevskii mentioned a new and fascinating Poisson summation formula suggested by André Paul Guinand in . 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 . We show that it is coupled to the Epstein ζ function by a coupling discovered by Jean-Pierre Kahane and Szolem Mandelbrojt in .
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