Polynomial Averages Converge to the Product of Integrals

Details Polynomial Averages Converge to the Product of Integrals Polynomial Averages Converge to the Product of Integrals

2004-03-26

arxiv.org/abs/math/0403454v1

Mathematics

Dynamical Systems

37A30

Scientific paper

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.

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