Absolute continuity, Interpolation and the Lyapunov order

TL;DR

This paper extends a Nevanlinna-Pick theorem for Hardy algebras to include boundary points with absolute continuity, emphasizing the importance of the Lyapunov order in the analysis.

Contribution

It introduces a new interpolation result at boundary points for Hardy algebras, utilizing the Lyapunov order to enhance the existing theory.

Findings

Extended Nevanlinna-Pick theorem to boundary points

Demonstrated the role of Lyapunov order in interpolation

Provided new insights into boundary behavior of Hardy algebra representations

Abstract

We extend our Nevanlinna-Pick theorem for Hardy algebras and their representations to cover interpolation at the absolutely continuous points of the boundaries of their discs of representations. The Lyapunov order plays a crucial role in our analysis.