The Smirnov class for de Branges--Rovnyak spaces

TL;DR

This paper demonstrates that for rational functions b, the associated de Branges-Rovnyak spaces are contained within their Smirnov classes, using an explicit construction.

Contribution

It provides an explicit construction showing the inclusion of de Branges-Rovnyak spaces into Smirnov classes for rational b, clarifying their relationship.

Findings

de Branges-Rovnyak spaces are contained in Smirnov classes for rational b

explicit construction method established

enhances understanding of function space relationships

Abstract

Using an explicit construction, we show that the de Branges-Rovnyak spaces $\mathscr{H}(b)$, corresponding to rational $b$, are contained in their associated Smirnov classes.