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

Voir la notice de l'article provenant de la source Cambridge University Press

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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