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Title:Divergence in Ergodic Theory
Author(s):Ayaragarnchanakul, Jantana C.
Doctoral Committee Chair(s):Josept M. Rosenblatt
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
Abstract:Let (X, B , P) be a non-atomic probability space and let T be an invertible measure-preserving transformation of ( X, B , P). Fix a sequence (mk ) in Z and let f ∈ Lp( X), 1 ≤ p ≤ infinity. We know that, depending on what the powers are, the averages 1n k=1nfTmk x may or may not converge a.e. x ∈ X, and they may or may not stay bounded a.e. We consider the properties of sequences (Ln) of real numbers and ( wn) of positive integers so that 1Ln k=1wnf Tmkx and 1Lnsup 1≤k≤n1k j=1k fTmjx converge a.e. x ∈ X for any sequence (mk) in Z .
Issue Date:2001
Type:Text
Language:English
Description:117 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001.
URI:http://hdl.handle.net/2142/86783
Other Identifier(s):(MiAaPQ)AAI3023013
Date Available in IDEALS:2015-09-28
Date Deposited:2001


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