Nevanlinna-Pick interpolation for $C+BH^\infty$

TL;DR

This paper extends Nevanlinna-Pick interpolation to the algebra  + BH^\u221e, providing a classification of invariant subspaces and a formula for distances in this setting.

Contribution

It introduces a classification of invariant subspaces for  + BH^ and establishes an interpolation theorem analogous to Nevanlinna-Pick for this algebra.

Findings

Classified invariant subspaces of  + BH^.

Derived a distance formula in this algebra.

Proved an analogue of the Nevanlinna-Pick interpolation theorem.

Abstract

Given an inner function $B$ we classify the invariant subspaces of the algebra $H^\infty_B:=\mathbb{C}+BH^\infty$. We derive a formula in terms of these invariant subspaces for the distance of an element in $L^\infty$ to a certain weak*-closed ideal in $H^\infty_B$ and use this to prove an analogue of the Nevanlinna-Pick interpolation theorem.