Fourier transformable measures with weak Meyer set support and their lift to the cut-and-project scheme
Author
Faculty Advisor
Date
2023
Keywords
cut-and-project schemes, Fourier transform of measures, Meyer sets
Abstract (summary)
In this paper, we prove that given a cut-and-project scheme (G,H,L) and a compact window W⊆H, the natural projection gives a bijection between the Fourier transformable measures on G×H supported inside the strip L∩(G×W) and the Fourier transformable measures on G supported inside ⋏(W). We provide a closed formula relating the Fourier transform of the original measure and the Fourier transform of the projection. We show that this formula can be used to re-derive some known results about Fourier analysis of measures with weak Meyer set support.
Publication Information
Strungaru, N. (2023). Fourier transformable measures with weak Meyer set support and their lift to the cut-and-project scheme. Canadian Mathematical Bulletin, 66(3), 1044-1060. https://doi.org/10.4153/S0008439523000164
Notes
Item Type
Article
Language
Rights
Attribution (CC BY)
