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Pure point spectrum for dynamical systems and mean, Besicovitch and Weyl almost periodicity

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dc.contributor.authorLenz, Daniel
dc.contributor.authorSpindeler, Timo
dc.contributor.authorStrungaru, Nicolae
dc.date.accessioned2023-07-25T15:32:06Z
dc.date.available2023-07-25T15:32:06Z
dc.date.issued2023
dc.description.abstractWe consider metrizable ergodic topological dynamical systems over locally compact, σ - compact abelian groups. We study pure point spectrum via suitable notions of almost periodicity for the points of the dynamical system. More specifically, we characterize pure point spectrum via mean almost periodicity of generic points. We then go on and show how Besicovitch almost periodic points determine both eigenfunctions and the measure in this case. After this, we characterize those systems arising from Weyl almost periodic points and use this to characterize weak and Bohr almost periodic systems. Finally, we consider applications to aperiodic order.
dc.identifier.citationLENZ, D., SPINDELER, T., & STRUNGARU, N. (2023). Pure point spectrum for dynamical systems and mean, Besicovitch and Weyl almost periodicity. Ergodic Theory and Dynamical Systems, 1-45. doi:10.1017/etds.2023.14
dc.identifier.doihttps://doi.org/10.1017/etds.2023.14
dc.identifier.urihttps://hdl.handle.net/20.500.14078/3169
dc.language.isoen
dc.relation.urihttps://hdl.handle.net/20.500.14078/2130
dc.rightsAttribution (CC BY)
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectdiscrete spectrum
dc.subjectaperiodic order
dc.subjectalmost periodicity properties of generic points
dc.titlePure point spectrum for dynamical systems and mean, Besicovitch and Weyl almost periodicityen
dc.typeArticle

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