On Weighted Dirac Combs Supported Inside Model Sets

Original · EN

In this paper we prove that given a weakly almost periodic measure μ supported inside some model set Λ(W) with closed window W, then the strongly almost periodic component μₛ and the null weakly almost periodic component μ₀ are both supported inside Λ(W). As a consequence we prove that given any translation bounded measure ω, supported inside some model set, then each of the pure point diffraction spectrum γpp and the continuous diffraction spectrum γc is either trivial or have a relatively dense support.