Eigenvalues of Toeplitz minimal systems of finite topological rank

TL;DR

This paper characterizes measure-theoretic eigenvalues in Toeplitz minimal systems of finite topological rank, highlighting cases without continuous eigenfunctions, and provides examples illustrating various scenarios.

Contribution

It offers a new characterization of measure-theoretic eigenvalues in Toeplitz systems of finite topological rank, including cases lacking continuous eigenfunctions.

Findings

Identifies measure-theoretic eigenvalues not associated with continuous eigenfunctions.

Provides examples demonstrating different spectral behaviors.

Characterizes eigenvalues in Toeplitz minimal systems of finite topological rank.

Abstract

In this article we characterize measure theoretical eigenvalues of Toeplitz Bratteli-Vershik minimal systems of finite topological rank which are not associated to a continuous eigenfunction. Several examples are provided to illustrate the different situations that can occur.