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On the Fourier Transformability of Strongly Almost Periodic Measures
- Part of
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- Journal:
- Canadian Journal of Mathematics / Volume 72 / Issue 4 / August 2020
- Published online by Cambridge University Press:
- 29 January 2019, pp. 900-927
- Print publication:
- August 2020
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- Article
- Export citation
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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.
