Interpolation in DE Branges-Rovnyak Spaces

Joseph A. Ball
Vladimir Bolotnikov, William & Mary
Sanne Ter Horst

Abstract

A general interpolation problem with operator argument is studied for functions f from the de Branges-Rovnyak space H(K(s)) associated with an analytic function s mapping the open unit disk D) into the closed unit disk. The interpolation condition is taken in the Rosenblum-Rovnyak form f(A)c = b (with a suitable interpretation of f(A)c) for given Hilbert space operator A and two vectors b, c from the same space.