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Tempered distributions with translation bounded measure as Fourier transform and the generalized Eberlein decomposition

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dc.contributor.authorSpindeler, Timo
dc.contributor.authorStrungaru, Nicolae
dc.date.accessioned2025-03-17T21:23:48Z
dc.date.available2025-03-17T21:23:48Z
dc.date.issued2023
dc.description.abstractIn this paper, we study the class of tempered distributions whose Fourier transform is a translation bounded measure and show that each such distribution in has order at most 2d. We show the existence of the generalized Eberlein decomposition within this class of distributions, and its compatibility with all previous Eberlein decompositions. The generalized Eberlein decomposition for Fourier transformable measures and properties of its components are discussed. Lastly, we take a closer look at the absolutely continuous spectrum of measures supported on Meyer sets.
dc.identifier.citationSpindeler, T., & Strungaru, N. (2023). Tempered distributions with translation bounded measure as Fourier transform and the generalized Eberlein decomposition. Mathematische Nachrichten 297(2), 716-740. https://doi.org/10.1002/mana.202100658
dc.identifier.doihttps://doi.org/10.1002/mana.202100658
dc.identifier.urihttps://hdl.handle.net/20.500.14078/3841
dc.language.isoen
dc.rightsAttribution-NonCommercial-NoDerivs (CC BY-NC-ND)
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectalmost periodic measures
dc.subjectFourier transform of measures
dc.subjectLebesgue decomposition
dc.titleTempered distributions with translation bounded measure as Fourier transform and the generalized Eberlein decompositionen
dc.typeArticle

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