| eBook ISBN: | 978-1-4704-2879-2 |
| Product Code: | MEMO/241/1143.E |
| List Price: | $79.00 |
| MAA Member Price: | $71.10 |
| AMS Member Price: | $47.40 |
| eBook ISBN: | 978-1-4704-2879-2 |
| Product Code: | MEMO/241/1143.E |
| List Price: | $79.00 |
| MAA Member Price: | $71.10 |
| AMS Member Price: | $47.40 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 241; 2015; 86 ppMSC: Primary 37; 22; 05
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.
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Table of Contents
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Chapters
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1. Introduction
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2. Preliminaries
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3. Nilsystems
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4. Generalized polynomials
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5. Nil Bohr$_0$-sets and generalized polynomials: Proof of Theorem B
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6. Generalized polynomials and recurrence sets: Proof of Theorem C
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7. Recurrence sets and regionally proximal relation of order $d$
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8. $d$-step almost automorpy and recurrence sets
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A.
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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.
-
Chapters
-
1. Introduction
-
2. Preliminaries
-
3. Nilsystems
-
4. Generalized polynomials
-
5. Nil Bohr$_0$-sets and generalized polynomials: Proof of Theorem B
-
6. Generalized polynomials and recurrence sets: Proof of Theorem C
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7. Recurrence sets and regionally proximal relation of order $d$
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8. $d$-step almost automorpy and recurrence sets
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A.
