On Dirichlet-type and n-isometric shifts in finite rank de Branges-Rovnyak spaces
In this paper, we study the function spaces D(μ) by Richter (1991) and Aleman (1993), and Dμ→ by Rydhe (2019). It is known that the forward shift Mz is bounded and expansive on D(μ), and therefore D(μ) coincides with a de Branges-Rovnyak space H[B]. We show that such a B is rational if and only if μ is finitely atomic, and this happens exactly when the corresponding defect operator has finite rank
