Israel Journal of Mathematics

, Volume 148, Issue 1, pp 267–276

Polynomial averages converge to the product of integrals

Authors

    • Department of Mathematics, McAllister BuildingThe Pennsylvania State University
  • Bryna Kra
    • Department of Mathematics, McAllister BuildingThe Pennsylvania State University
Article

DOI: 10.1007/BF02775439

Cite this article as:
Frantzikinakis, N. & Kra, B. Isr. J. Math. (2005) 148: 267. doi:10.1007/BF02775439

Abstract

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 inL 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.

Copyright information

© The Hebrew University Magnes Press 2005