Nevanlinna counting functions and pull-back measures on maximal ideal space of $H^\infty$

TL;DR

This paper explores the relationship between Nevanlinna counting functions and pull-back measures for analytic self-maps of the unit disk, emphasizing their significance on the maximal ideal space of bounded analytic functions.

Contribution

It provides precise characterizations of the connection between Nevanlinna counting functions and pull-back measures on the maximal ideal space.

Findings

Established detailed relations between Nevanlinna counting functions and pull-back measures.

Highlighted the importance of these concepts on the maximal ideal space.

Provided new insights into boundary behavior of analytic self-maps.

Abstract

In this paper we give precise characterizations of the relation between the Nevanlinna counting function and pull-back measure of an analytic self-map of the unit disk near the boundary. We show that it is quite worth considering these two concepts on the maximal ideal space of the bounded analytic functions.