Almost Periodic Szeg\H{o} Cocycles with Uniformly Positive Lyapunov Exponents

TL;DR

This paper constructs examples of almost periodic Verblunsky coefficients demonstrating that Herman's subharmonicity argument can ensure the associated Lyapunov exponents are uniformly positive, advancing understanding in spectral theory.

Contribution

It introduces specific almost periodic Verblunsky coefficients where Herman's subharmonicity method guarantees uniformly positive Lyapunov exponents, a novel application in spectral analysis.

Findings

Lyapunov exponents are uniformly positive for the constructed examples

Herman's subharmonicity argument applies to these almost periodic coefficients

Advances understanding of spectral properties in almost periodic settings

Abstract

We exhibit examples of almost periodic Verblunsky coefficients for which Herman's subharmonicity argument applies and yields that the associated Lyapunov exponents are uniformly bounded away from zero.