Fibonacci, Pavel Kurasov and Peter Sarnak

An atomic measure μ is a crystalline measure if it is supported by a locally finite set and if the distributional Fourier transform ^µ of μ is also an atomic measure supported by a locally finite set. Pavel Kurasov and Peter Sarnak recently constructed a crystalline measure whose supportis a Delone set and which is not a generalized Dirac comb. We show that this result is a direct consequence of the remarkable properties of a variant of the Fibonacci sequence.