# Weyl families of essentially unitary pairs

## TL;DR

This paper extends the classification of Weyl families associated with boundary pairs from unitary to essentially unitary cases, showing their closures belong to the Nevanlinna class, thus broadening the understanding of their spectral properties.

## Contribution

It generalizes the known classification of Weyl families from unitary to essentially unitary boundary pairs, establishing their membership in the Nevanlinna class.

## Key findings

- Closures of Weyl family members belong to the Nevanlinna class
- Bounded Weyl functions of essentially unitary pairs are in class []
- Extension of classification results to a broader class of boundary 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 $\mathcal{R}[\mathcal{H}]$.