Weyl families of essentially unitary pairs

Abstract

It is known that the Weyl families corresponding to unitary boundary pairs $(\mathcal{H},\Gamma)$ belong to the class $\tilde{\mathcal{R}}(\mathcal{H})$ of Nevanlinna families. Here we extend the theorem to the case of essentially unitary boundary pairs by showing that the closures of members of the Weyl families belong to the class $\tilde{\mathcal{R}}(\mathcal{H})$. Thus bounded Weyl functions of essentially unitary boundary pairs are of class $\mathcal{R}[\mathcal{H}]$.