Diffraction theory and almost periodic distributions

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dc.contributor.authorStrungaru, Nicolae
dc.contributor.authorTerauds, Venta
dc.date.accessioned2021-01-14
dc.date.accessioned2022-05-31T01:43:05Z
dc.date.available2022-05-31T01:43:05Z
dc.date.issued2016
dc.description.abstractWe introduce and study the notions of translation bounded tempered distributions, and autocorrelation for a tempered distrubution. 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 Lesbegue 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.
dc.format.extent362.60KB
dc.format.mimetypePDF
dc.identifier.citationStrungaru, N., & Terauds, V. (2016). Diffraction theory and almost periodic distributions. arXiv:1603.04796v1. https://arxiv.org/abs/1603.04796
dc.identifier.urihttps://hdl.handle.net/20.500.14078/2131
dc.languageEnglish
dc.language.isoen
dc.rightsAll Rights Reserved
dc.subjecttempered distributions
dc.subjectautocorrelation
dc.subjectalmost periodicity
dc.titleDiffraction theory and almost periodic distributions
dc.typeReport
dspace.entity.type
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