On spectral multiplicities of Gaussian actions

摘要

For any set $M$ of natural numbers there are mixing Gaussian automorphismsand non-mixing Gaussian automorphisms with singular spectrum (as well as someautomorphisms which are disjoint from all Gaussian actions) such that $M\cup\{\infty\}$ is the set of their spectral multiplicities. We show also thatfor a Gaussian flow $\{G_t\}$ the sets of spectral multiplicities for someautomorphisms $G_t$, $t>0$, could be different.