Strungaru, Nicolae2023-07-252023-07-252023Strungaru, 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/S0008439523000164https://hdl.handle.net/20.500.14078/3168In 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.enAttribution (CC BY)cut-and-project schemesFourier transform of measuresMeyer setsArticlehttps://doi.org/10.4153/S0008439523000164