Strungaru, Nicolae2020-10-052022-05-312022-05-312014Strungaru, N. “On weighted Dirac combs supported inside model sets”, J. Phys. A: Math. Theor. 47 (2014).https://hdl.handle.net/20.500.14078/1761In this paper we prove that given a weakly almost periodic measure μ supported inside some model set $\Lambda (W)$ with closed window W, then the strongly almost periodic component ${{\mu }_{S}}$ and the null weakly almost periodic component μ0 are both supported inside $\Lambda (W)$. 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 ${{\hat{\gamma }}_{{\rm pp}}}$ and the continuous diffraction spectrum ${{\hat{\gamma }}_{c}}$ is either trivial or has a relatively dense support.enAll Rights ReservedMeyer setsmodel setsalmost periodic measuresdiffractionBragg spectraArticlehttps://doi.org/10.1088/1751-8113/47/33/335202