Schur-Nevanlinna parameters, Riesz bases, and compact Hankel operators on the model space

Abstract

We study Riesz bases/Riesz sequences of reproducing kernels in the model space $K_\theta$ in connection with the corresponding Schur--Nevanlinna parameters and functions. In particular, we construct inner functions with given Schur--Nevanlinna parameters at a given sequence $\Lambda$ such that the corresponding systems of projections of reproducing kernels in the model space are complete/non complete. Furthermore, we give a compactness criterion for Hankel operators with symbol $\theta\overline B$, where $\theta$ is an inner function and $B$ is an interpolating Blaschke product and use this criterion to describe Riesz bases $\mathcal K_{\Lambda, \theta}$, with $\lim_{\lambda \in \Lambda, |\lambda| \to 1} \theta(\lambda) =0$.