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Andreu Ferre Moragues Thesis.pdf (1.35 MB)
ETD Abstract Container
Abstract Header
Properties of Furstenberg systems and multicorrelation sequences
Author Info
Ferre Moragues, Andreu
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1624314760948528
Abstract Details
Year and Degree
2021, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
In this dissertation we investigate two objects of central importance in ergodic theory: Furstenberg systems and multicorrelation sequences, as well as their interactions with combinatorics. This work is comprised of two main parts. In the first part we study Furstenberg systems. Among other things, we obtain a uniqueness theorem for Furstenberg systems and a characterization of countable weakly mixing amenable groups. In the second part we look at multicorrelation sequences for commuting measure preserving transformations. Under some ergodicity assumptions we show that a multicorrelation sequence has a decomposition of the form "structured part" plus an "error part". A close analysis of the methods used also yields results regarding sets of large returns as well as joint ergodicity.
Committee
Vitaly Bergelson (Advisor)
Daniel Thompson (Committee Member)
Alexander Leibman (Committee Member)
Pages
129 p.
Subject Headings
Mathematics
Keywords
Furstenberg systems, multicorrelation sequences, weakly mixing groups, large returns, joint ergodicity
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Citations
Ferre Moragues, A. (2021).
Properties of Furstenberg systems and multicorrelation sequences
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1624314760948528
APA Style (7th edition)
Ferre Moragues, Andreu.
Properties of Furstenberg systems and multicorrelation sequences.
2021. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1624314760948528.
MLA Style (8th edition)
Ferre Moragues, Andreu. "Properties of Furstenberg systems and multicorrelation sequences." Doctoral dissertation, Ohio State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1624314760948528
Chicago Manual of Style (17th edition)
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Document number:
osu1624314760948528
Download Count:
141
Copyright Info
© 2021, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.