On the Fourier Transformability of Strongly Almost Periodic Measures

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....

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Bibliographic Details
Published inCanadian journal of mathematics Vol. 72; no. 4; pp. 900 - 927
Main Author Strungaru, Nicolae
Format Journal Article
LanguageEnglish
Published Canada Canadian Mathematical Society 01.08.2020
Cambridge University Press
Subjects
Fourier transforms
Mathematics
almost periodic measure
43A25
Fourier transform of measures
43A05
42A75
43A60
Fourier-Bohr series
Eberlein decomposition
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Summary: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.
ISSN:0008-414X
1496-4279
DOI:10.4153/S0008414X19000075