Uniqueness theory for model sets, and spectral superresolution

Abstract

We build on the work of Basarab Matei by proving a new uniqueness theorem for some complex Radon measures whose Fourier transforms vanish on the model sets formulated by Yves Meyer. Although apparently specialized, it fits naturally into the broad areas of the extension problem for positive definite functions, spectral estimation, and spectral super-resolution. Out technology involves Kronecker’s theorem and a result in the mold of Chebatorev’s theorem, although essentially different from it.