Primitive Averages, Directional Expansivity, and Quantitative Twisted Recurrence for Ergodic ${\mathbb{Z}}^d$-Actions

Rickard Cullman, Sean Skinner

We prove two new results about probability preserving actions $T:{\mathbb{Z}}^d\curvearrowright (X,\hat{I}¼)$. First, for a function $f\in L^2(\hat{I}¼)$, we provide an explicit formula for the…