Some finite-dimensional backward-shift-invariant subspaces in the ball and a related interpolation problem

Abstract

We solve Gleason's problem in the reproducing kernel Hilbert space with reproducing kernel 1/(1- ∑1N zjw*j). We define and study some finite-dimensional resolvent-invariant subspaces that generalize the finite-dimensional de Branges-Rovnyak spaces to the setting of the ball.