Uniqueness theory for model sets, and spectral superresolution
type: Item
instance of: scholarly article
title: Uniqueness theory for model sets, and spectral superresolution
zbMATH Open document ID: 1467.42014
DOI: 10.4171/RLM/929
author: John J. Benedetto
author: Chenzhi Zhao
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2021-07-02T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 42B10
Mathematics Subject Classification ID: 46E27
zbMATH DE Number: 7367186
zbMATH Keywords: model sets
zbMATH Keywords: uniqueness theorems
zbMATH Keywords: spectral sampling data
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.4171/rlm/929
OpenAlex ID: W4244968416
description: scientific article; zbMATH DE number 7367186