Temperate distributions with locally finite support and spectrum on Euclidean spaces (Q6165187)

Let \(\mu\) be a measure of \(\mathbb{R}^d\) such that \(\mu\) and its Fourier transform \(\widehat{\mu}\) have discrete supports. In the theory of Fourier quasicrystals, there are some results giving sufficient conditions for \(\operatorname{supp}\mu\) to be a finite union of full-rank lattices (or contained in a finite union of full-rank lattices). In the paper, these results are generalised to a wide class of temperate distributions.