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Multidimensional Khintchine-Marstrand-type Problems
Easwaran, Hiranmoy

2012, Doctor of Philosophy, Ohio State University, Mathematics.
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 Lp-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.
Vitaly Bergelson, Ph.D. (Advisor)
Alexander Leibman, Ph.D. (Committee Member)
Nimish Shah, Ph.D. (Committee Member)
90 p.

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Easwaran, H. (2012). Multidimensional Khintchine-Marstrand-type Problems. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Easwaran, Hiranmoy. "Multidimensional Khintchine-Marstrand-type Problems." Electronic Thesis or Dissertation. Ohio State University, 2012. OhioLINK Electronic Theses and Dissertations Center. 26 Sep 2017.

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Easwaran, Hiranmoy "Multidimensional Khintchine-Marstrand-type Problems." Electronic Thesis or Dissertation. Ohio State University, 2012. https://etd.ohiolink.edu/

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