Spectral multiplicities for ergodic flows
Alexandre I. Danilenko Mariusz Lemańczyk
Discrete & Continuous Dynamical Systems - A 2013, 33(9): 4271-4289 doi: 10.3934/dcds.2013.33.4271
Let $E$ be a subset of positive integers such that $E\cap\{1,2\}\ne\emptyset$. A weakly mixing finite measure preserving flow $T=(T_t)_{t\in\Bbb R}$ is constructed such that the set of spectral multiplicities (of the corresponding Koopman unitary representation generated by $T$) is $E$. Moreover, for each non-zero $t\in\Bbb R$, the set of spectral multiplicities of the transformation $T_t$ is also $E$. These results are partly extended to actions of some other locally compact second countable Abelian groups.
keywords: Ergodic flow spectral multiplicities.

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