Ergodic Abelian actions with homogeneous spectrum

Abstract

It is shown that for each $N>0$ and for a wide class of Abelian non-compact locally compact second countable groups $G$ including all infinite countable discrete ones and ${\mathbb{R}}^{d_1}\times {\mathbb{Z}}^{d_2}$ with $d_1,d_2\ge 0$, there exists a weakly mixing probability preserving $G$-action with a homogeneous spectrum of multiplicity $N$.