Geodesic
On the Fourier Transformability of Strongly Almost Periodic Measures
Canadian journal of mathematics, Tome 72 (2020) no. 4, pp. 900-927

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DOI

In this paper we characterize the Fourier transformability of strongly almost periodic measures in terms of an integrability condition for their Fourier–Bohr series. We also provide a necessary and sufficient condition for a strongly almost periodic measure to be the Fourier transform of a measure. We discuss the Fourier transformability of a measure on $\mathbb{R}^{d}$ in terms of its Fourier transform as a tempered distribution. We conclude by looking at a large class of such measures coming from the cut and project formalism.
DOI : 10.4153/S0008414X19000075
Mots-clés : Fourier transform of measures, almost periodic measure, Fourier-Bohr series, Eberlein decomposition 
Strungaru, Nicolae. On the Fourier Transformability of Strongly Almost Periodic Measures. Canadian journal of mathematics, Tome 72 (2020) no. 4, pp. 900-927. doi: 10.4153/S0008414X19000075
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     title = {On the {Fourier} {Transformability} of {Strongly} {Almost} {Periodic} {Measures}},
     journal = {Canadian journal of mathematics},
     pages = {900--927},
     year = {2020},
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