On new spectral multiplicities for ergodic maps

TL;DR

This paper demonstrates that any subset of positive integers containing 2 can be realized as the set of essential multiplicities for the Koopman operator of a weakly mixing ergodic transformation.

Contribution

It introduces a method to construct weakly mixing transformations with prescribed spectral multiplicity sets including 2.

Findings

Any subset of positive integers containing 2 can be realized as spectral multiplicities.

The construction applies to weakly mixing transformations.

The result broadens understanding of spectral multiplicity possibilities.

Abstract

It is shown that each subset of positive integers that contains 2 is realizable as the set of essential values of the multiplicity function for the Koopman operator of some weakly mixing transformation.