On the Fourier transformability of strongly almost periodic measures

Author
Strungaru, Nicolae
2017
Keywords
almost periodic measures , Fourier-Bohr series , Eberlein decomposition , Fourier transform of measures
Abstract (summary)
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.
Publication Information
Strungaru, N. (2017). On the Fourier transformability of strongly almost periodic measures. arXiv:1704.04778v2. https://arxiv.org/abs/1704.04778
Report
English