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

Abstract

In this paper, we prove that given a cut-and-project scheme $(G,H,\mathcal{L})$ and a compact window $W\subseteq H$, the natural projection gives a bijection between the Fourier transformable measures on $G\times H$ supported inside the strip $\cL \cap (G \times W)$ and the Fourier transformable measures supported inside $\oplam(W)$, and relate their Fourier transforms. We use this formula to relate the Fourier transforms of the measures, and explain how one can use this relation to re-derive some known results about Fourier analysis of measures with Meyer set support.

16 pages

References in corpus (3)

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