Inner functions in weighted Hardy spaces

TL;DR

This paper explores the properties and construction methods of inner functions within weighted Hardy spaces, extending classical results from the standard Hardy space to more general settings.

Contribution

It introduces a new approach to constructing analogues of finite Blaschke products in weighted Hardy spaces, broadening the understanding of inner functions in these contexts.

Findings

Developed a method to construct inner functions in weighted Hardy spaces.

Extended classical results on inner functions to more general weighted spaces.

Provided insights into the structure of inner functions beyond the standard Hardy space.

Abstract

Inner functions play a central role in function theory and operator theory on the Hardy space over the unit disk. Motivated by recent works of C. B\'en\'eteau et al. and of D. Seco, we discuss inner functions on more general weighted Hardy spaces and investigate a method to construct analogues of finite Blaschke products.