Polynomial Averages Converge to the Product of Integrals

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We answer a question posed by Vitaly Bergelson, showing that in a totally ergodic system, the average of a product of functions evaluated along polynomial times, with polynomials of pairwise differing degrees, converges in $L^{2}$ to the product of the integrals. Such averages are characterized by nilsystems and so we reduce the problem to one of uniform distribution of polynomial sequences on nilmanifolds.
37A30

Keywords

Dynamical Systems

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/70602

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0403454
 http://arxiv.org/abs/math/0403454

Collections

arXiv