Spectral multiplicities for ergodic flows (Q379574)

The paper considers mainly the following theorem. Let \(E\) be a subset of positive integers with \(E\cap\{1, 2\}\neq \emptyset\). {\parindent=6mm \begin{itemize}\item[1)] There is a weakly mixing finite measure preserving flow \(T=(T_t)_{t\in\mathbb{R}}\) with the set of spectral multiplicities of the Koopman unitary representation generated by \(T\) is \(E\). \item[2)] For each non-zero \(t\in \mathbb{R}\), the set of spectral multiplicities of the Koopman operator generated by the transformation \(T_t\) is also \(E\). NEWLINENEWLINE\end{itemize}} In Sections 2--6 there is some material to understand the techniques used in Sections 1 and 7.NEWLINENEWLINEOn the final Section 7, the main theorem is extended to actions of other non-compact Abelian groups: groups without non-trivial compact subgroups, connected groups, and others.