De Branges-Rovnyak spaces generated by row Schur functions with mate

Abstract

In this paper, we study the de Branges-Rovnyak spaces H(B) generated by row Schur functions B with mate a. We prove that the polynomials are dense in H(B), and characterize the backward shift invariant subspaces of H(B). We then describe the cyclic vectors in H(B) when B is of finite rank and dim⁡(aH2)⊥<∞.