On the Fourier Transformability of Strongly Almost Periodic Measures. (29th August 2020)

• Record Type: Journal Article
• Authors: Strungaru, Nicolae
• Is Part Of: Canadian journal of mathematics. Volume 72:Number 4(2020)
• Page Start: 900
• Page End: 927
• Publication Date: 2020-08-29
• Subjects: 43A05, -- 43A60, -- 43A25, -- 42A75; Fourier transform of measures, -- almost periodic measure, -- Fourier-Bohr series, -- Eberlein decomposition; Mathematics -- Periodicals; Mathematics; Electronic journals; Periodicals; 510
• DOI: 10.4153/S0008414X19000075
• Languages: English
• ISSNs: 0008-414X

Abstract

Abstract: 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.