Nil Bohr-Sets and Almost Automorphy of Higher Order (Memoirs of the American Mathematical Society) - Softcover

Huang, Wen; Shao, Song; Ye, Xiangdong

Softcover

ISBN 10: 147041872X ISBN 13: 9781470418724

Publisher: American Mathematical Society, 2016

Synopsis

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.

About this title

About the Author

Wen Huang, Song Shao, and Xiangdong Ye, University of Science and Technology of China, Hefei, Anhui, China.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2016
• ISBN 10: 147041872X
• ISBN 13: 9781470418724
• Binding: Paperback
• Language: English
• Number of pages: 86