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 pG, H, Lq and a compact window W Ď H, the natural projection gives a bijection between the Fourier transformable measures on G ˆH supported inside the strip L X pG ˆW q and the Fourier transformable measures supported inside NpWq, 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.