On the maximal spectral type of nilsystems

Ethan Ackelsberg, Florian K. Richter, Or Shalom

Let $(G/\Gamma ,R_a)$ be an ergodic $k$-step nilsystem for $k\ge 2$. We adapt an argument of Parry to show that $L^2(G/\Gamma )$ decomposes as a sum of a subspace with discrete spectrum and a…