Date of Award

1-1-2009

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Mathematics and Statistics

Content Description

1 online resource (v, 44 pages) : illustrations.

Dissertation/Thesis Chair

Karin Reinhold

Committee Members

Martin Hildebrand, Richard O'Neil, Michael Stessin

Keywords

Convolutions (Mathematics), Probability measures, Convergence

Subject Categories

Physical Sciences and Mathematics

Abstract

Let $(X,\mathcal{B},m,\tau)$ be a dynamical system with $(X,\mathcal{B},m)$ a probability space and $\tau$ a measurable, invertible, measure preserving transformation. The present thesis deals with the almost everywhere convergence in $\mbox{L}^1(X)$ of a sequence of operators of weighted averages. Almost everywhere convergence follows once we obtain an appropriate maximal estimate and once we provide a dense class where convergence holds almost everywhere. The weights are convolution products of members of a sequence of probability measures $\{\nu_i\}$ on $\mathbb{Z}$. In the last section, we also prove a variation inequality for this type of sequence operators.

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