Skip to Main Content
Frequently Asked Questions
Submit an ETD
Global Search Box
Need Help?
Keyword Search
Participating Institutions
Advanced Search
School Logo
Files
File List
osu1343853458.pdf (629 KB)
ETD Abstract Container
Abstract Header
Multidimensional Khintchine-Marstrand-type Problems
Author Info
Easwaran, Hiranmoy
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1343853458
Abstract Details
Year and Degree
2012, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
This dissertation deals with multidimensional versions of the classical Khintchine conjecture on almost-everywhere convergence of certain averages originating in the theory of uniform distribution. We study analogous actions of multiplicative semigroups of rings and investigate both negative results extending Marstrand's answer to Khintchine's conjecture, and positive results answering related questions. We first show that L
p
-convergence holds very broadly for almost any sequence of averages for these actions. Next, we show that almost-everywhere convergence of averages taken over additive Følner sequences fails. Finally, we investigate what kinds of averages for these actions give pointwise convergence almost everywhere.
Committee
Vitaly Bergelson, Ph.D. (Advisor)
Alexander Leibman, Ph.D. (Committee Member)
Nimish Shah, Ph.D. (Committee Member)
Pages
90 p.
Subject Headings
Mathematics
Keywords
Khintchine
;
Khinchin
;
Marstrand
;
Gaussian integers
;
uniform distribution
;
pointwise ergodic theorem
;
mean ergodic theorem
;
semigroup
Recommended Citations
Refworks
EndNote
RIS
Mendeley
Citations
Easwaran, H. (2012).
Multidimensional Khintchine-Marstrand-type Problems
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1343853458
APA Style (7th edition)
Easwaran, Hiranmoy.
Multidimensional Khintchine-Marstrand-type Problems.
2012. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1343853458.
MLA Style (8th edition)
Easwaran, Hiranmoy. "Multidimensional Khintchine-Marstrand-type Problems." Doctoral dissertation, Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1343853458
Chicago Manual of Style (17th edition)
Abstract Footer
Document number:
osu1343853458
Download Count:
1,571
Copyright Info
© 2012, some rights reserved.
Multidimensional Khintchine-Marstrand-type Problems by Hiranmoy Easwaran is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by The Ohio State University and OhioLINK.