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arXiv · 1309.7947

On Weighted Dirac Combs Supported Inside Model Sets

Nicolae Strungaru
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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.

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Nicolae Strungaru. 2013-09-30. On Weighted Dirac Combs Supported Inside Model Sets. https://doi.org/10.1088/1751-8113%2F47%2F33%2F335202

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