Fourier Transformable Measures with Meyer set support and their lift to\n the cut and project scheme

2021/11/22 by Nicolae Strungaru, Strungaru, Nicolae
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2111.11569

openalex publication_date 2021/11/22 · openalex created_date 2022/11/02 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that given a cut-and-project scheme (G, H,\n\L) and a compact window W \⊆ H, the natural projection\ngives a bijection between the Fourier transformable measures on G \× H\nsupported inside the strip cL \∩ (G \× W) and the Fourier\ntransformable measures supported inside oplam(W), and relate their Fourier\ntransforms. We use this formula to relate the Fourier transforms of the\nmeasures, and explain how one can use this relation to re-derive some known\nresults about Fourier analysis of measures with Meyer set support.\n

Citations

• Pure point spectrum for dynamical systems and mean almost periodicity
• Model sets with precompact Borel windows

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