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    3. Nil Bohr-sets and Almost Automorphy of Higher Order

    Nil Bohr-sets and Almost Automorphy of Higher Order

    Posted By: DZ123
    Date: 6 Aug 2020 15:58:45
    Nil Bohr-sets and Almost Automorphy of Higher Order

    Wen Huang, Song Shao, Xiangdong Ye, "Nil Bohr-sets and Almost Automorphy of Higher Order"
    English | 2016 | ISBN: 147041872X | PDF | pages: 98 | 0.9 mb

    Two closely related topics, higher order Bohr sets and higher order almost automorphy, are investigated in this paper. Both of them are related to nilsystems. In the first part, the problem which can be viewed as the higher order version of an old question concerning Bohr sets is studied: for any $din mathbbN$ does the collection of $nin mathbbZ: Scap (S-n)capldotscap (S-dn)neq emptyset$ with $S$ syndetic coincide with that of Nil$d$ Bohr$0$-sets In the second part, the notion of $d$-step almost automorphic systems with $dinmathbbNcupinfty$ is introduced and investigated, which is the generalization of the classical almost automorphic ones.
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