Nevanlinna-Pick interpolation for $C+B{H}^{\infty }$

Abstract

Given an inner function $B$ we classify the invariant subspaces of the algebra $H_B^{\infty }:=\mathbb{C}+B{H}^{\infty }$. 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 $H_B^{\infty }$ and use this to prove an analogue of the Nevanlinna-Pick interpolation theorem.

19 pages, no figures

Cited by in corpus (2)

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• Abrahamse's interpolation theorem and Fuchsian groups