Fourier Uniqueness and Non-Uniqueness Pairs

Motivated by recent works by Radchenko and Viazovska and by Ramos and Sousa, we find sufficient conditions for a pair of discrete subsets of the real line to be a uniqueness or a non-uniqueness pair for the Fourier transform. These conditions are close to each other. The uniqueness result can be upg...

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Bibliographic Details
Date:2025
Main Authors: Kulikov, Aleksei, Nazarov, Fedor, Sodin, Mikhail
Format: Article
Language:English
Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України 2025
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Online Access:https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1095
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Journal Title:Journal of Mathematical Physics, Analysis, Geometry

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Journal of Mathematical Physics, Analysis, Geometry
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Summary:Motivated by recent works by Radchenko and Viazovska and by Ramos and Sousa, we find sufficient conditions for a pair of discrete subsets of the real line to be a uniqueness or a non-uniqueness pair for the Fourier transform. These conditions are close to each other. The uniqueness result can be upgraded to an interpolation formula, which in turn produces an abundance of discrete measures with discrete Fourier transform. Mathematical Subject Classification 2020: 42A99