A characterization of Schur multipliers between character-automorphic Hardy spaces

TL;DR

This paper provides a new characterization of character-automorphic Hardy spaces of order 2 and their contractive multipliers using de Branges Rovnyak spaces, leveraging analytic extension and matrix function factorization techniques.

Contribution

It introduces a novel characterization of these Hardy spaces and their multipliers, connecting them with de Branges Rovnyak spaces and advanced factorization methods.

Findings

New characterization of character-automorphic Hardy spaces of order 2

Representation of contractive multipliers via de Branges Rovnyak spaces

Application of Leech's matrix-valued analytic function factorization

Abstract

We give a new characterization of character-automorphic Hardy spaces of order 2 and of their contractive multipliers in terms of de Branges Rovnyak spaces. Keys tools in our arguments are analytic extension and a factorization result for matrix-valued analytic functions due to Leech.