Spectral multiplicities for infinite measure preserving transformations

TL;DR

This paper demonstrates that for any subset of natural numbers, there exists an ergodic infinite measure-preserving transformation whose Koopman operator has that subset as its essential multiplicity values.

Contribution

It constructs transformations with prescribed essential multiplicity sets, expanding understanding of spectral multiplicities in infinite measure systems.

Findings

Any subset of natural numbers can be realized as spectral multiplicity set.

The construction applies to ergodic conservative infinite measure-preserving transformations.

It advances the classification of spectral types in infinite ergodic theory.

Abstract

Each subset $E\subset\Bbb N$ is realized as the set of essential values of the multiplicity function for the Koopman operator of an ergodic conservative infinite measure preserving transformation.