Abstract
In this article we will extend 'the weak mixing theorem' for certain locally compact Polish groups (Moore groups and minimally weakly mixing groups). In addition, we will show that the Gaussian action associated with the infinite-dimensional irreducible representation of the continuous Heisenberg group, H3(ℝ), is weakly mixing but not mildly mixing.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 794-815 |
| Number of pages | 22 |
| Journal | Ergodic Theory and Dynamical Systems |
| Volume | 36 |
| Issue number | 3 |
| DOIs | |
| State | Published - May 1 2016 |
Funding
This work is based on the author's master thesis. The author would like to personally thank her MSc adviser, Jon Aaronson, for acquainting her with the world of dynamics, and affording her guidance and patience. Also, to Dror Speiser who drew the author's attention to the fact that the infinite dihedral group and the quaternion group are both infinite non-abelian Moore groups. Many thanks are also given to Eli Glasner, Benjamin Weiss and Alexandre I. Danilenko for finding mistakes in previous versions. Last but not least, to Tom Meyerovitch, Zemer Kosloff and Michael Bromberg for useful conversations. Their support and contributions are greatly appreciated. This work has been partially supported by I.S.F. grant numbers 1114/08 and 1157/08.
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics