On spectral multiplicities {2, 4,..., 2^n} for totally ergodic Z^2-actions

TL;DR

This paper investigates the spectral multiplicities of tensor products of totally ergodic Z^2-actions, establishing conditions under which specific sets of multiplicities appear, including for mixing actions through a limit approach.

Contribution

It extends the understanding of spectral multiplicities in ergodic theory by characterizing sets {2, 4, ..., 2^n} for tensor products and applying limit procedures to mixing actions.

Findings

Spectral multiplicities {2, 4, ..., 2^n} are achievable for tensor products of totally ergodic Z^2-actions.

Conditions are identified under which similar spectral multiplicity sets occur in mixing actions.

A limit procedure is used to extend results to mixing actions.

Abstract

For totally ergodic Z^2-actions a collection of weak limits provide the set {2,4, ..., 2 ^ n} of spectral multiplicities for their tensor product. Our conditions allow to obtain a similar result for mixing actions via some limit procedure.