On Weighted Dirac Combs Supported Inside Model Sets

Abstract

In this paper we prove that given a weakly almost periodic measure $\mu$ 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 ${\mu }_0$ are both supported inside $\Lambda (W)$. As a consequence we prove that given any translation bounded measure $\omega$, supported inside some model set, then each of the pure point diffraction spectrum ${\hat{\gamma }}_{pp}$ and the continuous diffraction spectrum ${\hat{\gamma }}_c$ is either trivial or have a relatively dense support.

18 pages

References in corpus (2)

• Pure point diffraction and cut and project schemes for measures: The smooth case
• Positive Positive Definite Discrete Strong Almost Periodic Measures and Bragg Diffraction

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