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arXiv · 0908.1643

Mixing constructions with infinite invariant measure and spectral multiplicities

Alexandre I. Danilenko·Valery V. Ryzhikov
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Abstract

We introduce high staircase infinite measure preserving transformations and prove that they are mixing under a restricted growth condition. This is used to (i) realize each subset $E\subset\Bbb N\cup\{\infty\}$ as the set of essential values of the multiplicity function for the Koopman operator of a mixing ergodic infinite measure preserving transformation, (ii) construct mixing power weakly mixing infinite measure preserving transformations, (iii) construct mixing Poissonian automorphisms with a simple spectrum, etc.

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Alexandre I. Danilenko, Valery V. Ryzhikov. 2009-08-12. Mixing constructions with infinite invariant measure and spectral multiplicities. https://arxiv.org/abs/0908.1643

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