On extreme points of measures which implement an isometric embedding of model spaces

TL;DR

This paper characterizes the extreme points of measures implementing isometric embeddings of model spaces, focusing on finite Blaschke products and providing partial results for general inner functions.

Contribution

It identifies all extreme points for measures associated with finite Blaschke products and offers partial insights for more general inner functions.

Findings

Complete characterization for finite Blaschke products.

Partial results for generic inner functions.

Advances understanding of measures in isometric embeddings.

Abstract

In 1996 A. Alexandrov solved an isometric embedding problem for model spaces $K_\Theta$ with an arbitrary inner function $\Theta$. We find all extreme points of this convex set of measures in the case when $\Theta$ is a finite Blaschke product, and obtain some partial results for generic inner functions.