Interpolation in de Branges-Rovnyak spaces defined by a non-extreme rational function

We provide a characterization of universal and multiplier interpolating sequences for de Branges-Rovnyak spaces where the defining function is a non-extreme, rational function. Previous work on this topic examined interpolation in de Branges-Rovnyak spaces specifically in cases where the space coincides with a local Dirichlet space under norm equivalence. The more general setting we are interested in here corresponds to higher order local Dirichlet spaces recently investigated by Gu, Luo and Richter. In this general setting we characterize universal interpolating sequences and show that they coincide with multiplier interpolating sequences. We also explore random interpolation through the use of Steinhaus sequences.

This is work in progress with A. Hartmann.