Concrete examples of $\mathscr{H}(b)$ spaces

TL;DR

This paper provides explicit descriptions of de Branges-Rovnyak spaces (b) for specific rational outer functions raised to positive powers, enhancing understanding of these functional spaces.

Contribution

It offers a new explicit characterization of (b) spaces when b is a rational outer function raised to a positive power, a case not previously detailed.

Findings

Explicit descriptions of (b) spaces for q^r where q is rational outer

Enhanced understanding of the structure of (b) spaces in this specific case

Potential applications in operator theory and function spaces

Abstract

In this paper we give an explicit description of de Branges-Rovnyak spaces $\HH(b)$ when $b$ is of the form $q^{r}$, where $q$ is a rational outer function in the closed unit ball of $H^{\infty}$ and $r$ is a positive number.