# A Note on multipliers between model spaces

## TL;DR

This paper investigates the conditions under which multipliers between different model spaces are non-trivial, utilizing Beurling--Malliavin densities and recent advances in Toeplitz operator theory.

## Contribution

It provides necessary and sufficient conditions for non-trivial multipliers between model spaces with meromorphic inner functions, connecting to Toeplitz operator injectivity.

## Key findings

- Conditions involving Beurling--Malliavin densities for non-trivial multipliers
- Linking multipliers to Toeplitz operator injectivity
- Characterization of multipliers for meromorphic inner functions

## Abstract

In this note, we study the multipliers from one model space to another. In the case when the corresponding inner functions are meromorphic, we give both necessary and sufficient conditions ensuring this set of multipliers is not trivial. Our conditions involve the Beurling--Malliavin densities and are based on the deep work of Makarov--Poltoratski on injectivity of Toeplitz operators.