New spectral multiplicities for mixing transformations

TL;DR

This paper demonstrates that for any subset of natural numbers containing 1 or 2, there exists a mixing transformation with spectral multiplicities exactly matching that set.

Contribution

It introduces a method to construct mixing transformations with prescribed spectral multiplicities, expanding the understanding of spectral properties in ergodic theory.

Findings

Existence of mixing transformations with spectral multiplicities containing 1 or 2

Construction techniques for specific spectral multiplicity sets

Advancement in spectral theory of dynamical systems

Abstract

It is shown that if $E$ is any subset of $\Bbb N$ such that either $1\in E$ or $2\in E$ then there is a mixing transformation whose set of spectral multiplicities is $E$.