Ergodic automorphisms with simple spectrum characterized by fast correlation decay

A. A. Prikhod'ko

Published 2013-01-13Version 1

The existence of measure preserving invertible transformations $T$ with simple spectrum is established possessing the following rate of correlation decay $(f(T^k x), f(x)) = O(|k|^{-1/2+{\epsilon}})$ for a dense family of functions $f$ and any ${\epsilon > 0}$.