EVENT DETAILS AND ABSTRACT

Title: Almost Everywhere Convergence and the Work of Alexandra Bellow
Speaker: Roger Jones
Speaker Info: DePaul University
Brief Description:
Special Note:
Abstract:

Alexandra Bellow has written a number of very interesting papers, and posed a number of questions, during her career. She was the first person to show that the ergodic averages along any lacunary sequence will diverge for some function in L1. She, with her coauthor, Viktor Losert, were the first to exhibit a sequence of density zero along which the ergodic averages will converge a.e. for all f ∈ L1. She was the first person to ask about convergence of ergodic averages along the sequence of squares, and was the first person to show that given p1 ≥ 1 and p0 > p1, there is a subsequence such that the ergodic averages converge for all f ∈ Lp0 but diverge for some f ∈ Lp1 . These results, and others, have resulted in subsequent papers by a number of other authors. Thus her work has had a considerable impact on the field of almost everywhere convergence in ergodic theory. This talk will examine the development of some of her work. In particular we will talk about the paper on moving averages, which came about while trying to find a way to approach the problem about convergence of ergodic averages along the sequence of squares. The proof in the final version of the moving averages paper is very different from the initial proof, and resulted in a stronger theorem. Modifi- cations of the initial proof resulted in finding conditions that imply convergence of convolution powers of a measure, as well as a number of other results.