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arXiv · 1406.3321

On spectral multiplicities of Gaussian actions

V. V. Ryzhikov
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Abstract

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

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V. V. Ryzhikov. 2014-06-30. On spectral multiplicities of Gaussian actions. https://arxiv.org/abs/1406.3321

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