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arXiv · 1008.4845

Spectral multiplicities for ergodic flows

Alexandre I. Danilenko·Mariusz Lemańczyk
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Abstract

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.

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Alexandre I. Danilenko, Mariusz Lemańczyk. 2010-08-28. Spectral multiplicities for ergodic flows. https://arxiv.org/abs/1008.4845

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