000			03915nam a22004813i 4500
001			EBC4901862
003			MiAaPQ
005			20240729131324.0
006			m o d |
007			cr cnu||||||||
008			240724s2016 xx o ||||0 eng d
020			_a9781470428792 _q(electronic bk.)
020			_z9781470418724
035			_a(MiAaPQ)EBC4901862
035			_a(Au-PeEL)EBL4901862
035			_a(OCoLC)938502613
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA353.A9 H83 2015
082	0		_a515/.9
100	1		_aHuang, Wen.
245	1	0	_aNil Bohr-Sets and Almost Automorphy of Higher Order.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2016.
264		4	_c©2015.
300			_a1 online resource (98 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society Series ; _vv.241
505	0		_aCover -- Title page -- Chapter 1. Introduction -- 1.1. Higher order Bohr problem -- 1.2. Higher order almost automorphy -- 1.3. Further questions -- 1.4. Organization of the paper -- Chapter 2. Preliminaries -- 2.1. Basic notions -- 2.2. Bergelson-Host-Kra' Theorem and the proof of Theorem A(2) -- 2.3. Equivalence of Problems B-I,II,III -- Chapter 3. Nilsystems -- 3.1. Nilmanifolds and nilsystems -- 3.2. Nilpotent Matrix Lie Group -- Chapter 4. Generalized polynomials -- 4.1. Definitions -- 4.2. Basic properties of generalized polynomials -- Chapter 5. Nil Bohr₀-sets and generalized polynomials: Proof of Theorem B -- 5.1. Proof of Theorem B(1) -- 5.2. Proof of Theorem B(2) -- Chapter 6. Generalized polynomials and recurrence sets: Proof of Theorem C -- 6.1. A special case and preparation -- 6.2. Proof of Theorem C -- Chapter 7. Recurrence sets and regionally proximal relation of order -- 7.1. Regionally proximal relation of order -- 7.2. Nil_{ } Bohr₀-sets, Poincaré sets and \RP^{[ ]} -- 7.3. _{ }-sets and \RP^{[ ]} -- 7.4. Cubic version of multiple recurrence sets and \RP^{[ ]} -- 7.5. Conclusion -- Chapter 8. -step almost automorpy and recurrence sets -- 8.1. Definition of -step almost automorpy -- 8.2. Characterization of -step almost automorphy -- Appendix A. -- A.1. The Ramsey properties -- A.2. Compact Hausdorff systems -- A.3. Intersective -- Bibliography -- Index -- Back Cover.
520			_aTwo 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.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aAutomorphic functions.
650		0	_aFourier analysis.
655		4	_aElectronic books.
700	1		_aShao, Song.
700	1		_aYe, Xiangdong.
776	0	8	_iPrint version: _aHuang, Wen _tNil Bohr-Sets and Almost Automorphy of Higher Order _dProvidence : American Mathematical Society,c2016 _z9781470418724
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society Series
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4901862 _zClick to View
999			_c127898 _d127898