On the Fourier transformability of strongly almost periodic measures
almost periodic measures, Fourier-Bohr series, Eberlein decomposition, Fourier transform of measures
In this paper we characterize the Fourier transformability of a strongly almost periodic measure in terms of an integrability condition for its Fourier Bohr series. We also provide a necessary and sufficient condition for a strongly almost periodic measure to be a Fourier transform of a measure. We discuss the Fourier transformability of a measure on $\RR^d$ 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.
Strungaru, N. (2017). On the Fourier transformability of strongly almost periodic measures. arXiv:1704.04778v2. https://arxiv.org/abs/1704.04778
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