Mixing constructions with infinite invariant measure and spectral multiplicities

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 $E\subset \mathbb{N}\cup \{\infty \}$ 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.

References in corpus (3)

• Ergodic properties of Poissonian ID processes
• Spectral multiplicities for infinite measure preserving transformations
• New spectral multiplicities for mixing transformations

Cited by in corpus (1)

• Rank-one flows of transformations with infinite ergodic index