2018/08/06 by Benjamin Jaye, Jaye, Benjamin, Mishko Mitkovski +1
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1808.02149
openalex publication_date 2018/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper builds upon two key principles behind the Bourgain-Dyatlov quantitative uniqueness theorem for functions with Fourier transform supported in an Ahlfors regular set. We first provide a characterization of when a quantitative uniqueness theorem holds for functions with very quickly decaying Fourier transform, thereby providing an extension of the classical Paneah-Logvinenko-Sereda theorem. Secondly, we derive a transference result which converts a quantitative uniqueness theorem for functions with fast decaying Fourier transform to one for functions with Fourier transform supported on a fractal set. As well as recovering the result of Bourgain-Dyatlov, we obtain analogous uniqueness results for denser fractals.