Convergence in Ergodic Theory

We investigate two problems involving convergence in ergodic theory. The first problem is the following: Given a measure preserving transformation T and a weight function w(alpha) → 0 as alpha → 0, is there a p > 0 such that the expression w(alpha)#{ n : 1n k=1nfT kx >a } have a limit, a.s. or in norm, as alpha → 0 for all functions f ∈ Lp0 [0,1]? No, we show. Here # denotes counting measure and f's are taken to be mean-zero functions. We also consider similar questions for the more general operator w(alpha)#{n : 1nq k=1n f(Tk(x)) > alpha}, q > 1. The second problem addressed is to give arithmetic and probabilistic characterizations on the integer sequence ( nk) such that the series of ergodic differences k=1infinity ( Ank+1f-Ankf ), where An denotes the usual ergodic averages, converges unconditionally for all functions f in some Lp space.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Argiris, Georgios

Contributors dc:contributor

• Rosenblatt, Joseph

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI3023009

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86781