Smooth analytic functions and model subspaces

TL;DR

This survey explores the interplay between boundary-smooth analytic functions' factorization and model subspaces in Hardy spaces, highlighting their interrelationship and mutual influence.

Contribution

It provides a comprehensive overview of the connection between boundary-smooth function factorizations and invariant subspaces in Hardy spaces.

Findings

Detailed analysis of Riesz--Nevanlinna factorization in smooth analytic functions

Insights into the structure of model subspaces in Hardy spaces and BMOA

Highlighting the cross-fertilization between factorization and invariant subspaces

Abstract

The main themes of this survey are as follows: (a) the canonical (Riesz--Nevanlinna) factorization in various classes of analytic functions on the disk that are smooth up to its boundary, and (b) model subspaces (i.e., invariant subspaces of the backward shift) in the Hardy spaces $H^p$ and in BMOA. It is the interrelationship and a peculiar cross-fertilization between the two topics that we wish to highlight.