Uniqueness theory for model sets, and spectral superresolution (Q2039143)

Summary: We build on the work of \textit{B. Matei} [Asymptotic Anal. 97, No. 3--4, 291--299 (2016; Zbl 1404.42024)] by proving a new uniqueness theorem for some complex Radon measures whose Fourier transforms vanish on the model sets formulated by \textit{Y. Meyer} [Nombres de Pisot, nombres de Salem et analyse harmonique. Lect. Notes Math. 117 (1970; Zbl 0189.14301); Algebraic numbers and harmonic analysis. Amsterdam: Elsevier (North-Holland) (1972; Zbl 0267.43001)]. 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.