Nil Bohr-sets and almost automorphy of higher order
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Bibliographic Information
Nil Bohr-sets and almost automorphy of higher order
（Memoirs of the American Mathematical Society, no. 1143）
American Mathematical Society, 2016
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Includes bibliographical references
"Volume 241, number 1143 (fourth of 4 numbers), May 2016"
Description and Table of Contents
Description
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 $d\in \mathbb{N}$ does the collection of $\{n\in \mathbb{Z}: S\cap (S-n)\cap\ldots\cap (S-dn)\neq \emptyset\}$ 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 $d\in\mathbb{N}\cup\{\infty\}$ is introduced and investigated, which is the generalization of the classical almost automorphic ones.
Table of Contents
Introduction
Preliminaries
Nilsystems
Generalized polynomials
Nil Bohr$_0$-sets and generalized polynomials: Proof of Theorem B
Generalized polynomials and recurrence sets: Proof of Theorem C
Recurrence sets and regionally proximal relation of order $d$ $d$-step almost automorpy and recurrence sets
Appendix A
Bibliography
Index
by "Nielsen BookData"