Kotani-Last problem and Hardy spaces on surfaces of Widom type

TL;DR

This paper investigates a specific class of Jacobi matrices with purely absolutely continuous spectra, identifying an analytic condition on the resolvent set that explains this spectral property.

Contribution

It introduces a new analytic condition on the resolvent set that characterizes non almost periodic ergodic Jacobi matrices with pure absolutely continuous spectrum.

Findings

Identified an analytic condition responsible for the spectral property

Characterized a class of Jacobi matrices with pure absolutely continuous spectrum

Linked spectral behavior to resolvent set properties

Abstract

It is a small theory of non almost periodic ergodic families of Jacobi matrices with pure (however) absolutely continuous spectrum. And the reason why this effect may happen: under our "axioms" we found an analytic condition on the resolvent set that is responsible for (exactly equivalent to) this effect.