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Diffraction theory and almost periodic distributions

Citation

Strungaru, N and Terauds, V, Diffraction theory and almost periodic distributions, Journal of Statistical Physics, 164, (5) pp. 1183-1216. ISSN 0022-4715 (2016) [Refereed Article]


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DOI: doi:10.1007/s10955-016-1579-8

Abstract

We introduce and study the notions of translation bounded tempered distributions, and autocorrelation for a tempered distribution. We further introduce the spaces of weakly, strongly and null weakly almost periodic tempered distributions and show that for weakly almost periodic tempered distributions the Eberlein decomposition holds. For translation bounded measures all these notions coincide with the classical ones.We show that tempered distributions with measure Fourier transform are weakly almost periodic and that for this class, the Eberlein decomposition is exactly the Fourier dual of the Lebesgue decomposition, with the Fourier–Bohr coefficients specifying the pure point part of the Fourier transform. We complete the project by looking at few interesting examples.

Item Details

Item Type:Refereed Article
Keywords:tempered distributions, autocorrelation, diffraction, almost periodicity, Fourier transform, translation bounded distributions
Research Division:Mathematical Sciences
Research Group:Pure Mathematics
Research Field:Lie Groups, Harmonic and Fourier Analysis
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Terauds, V (Dr Venta Terauds)
ID Code:116631
Year Published:2016
Web of Science® Times Cited:1
Deposited By:Mathematics and Physics
Deposited On:2017-05-15
Last Modified:2017-05-15
Downloads:0

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