A Note on multipliers between model spaces

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.