Abstract Interpolation Problem and Some Applications. II: Coefficient Matrices

Abstract

The main content of this paper is Lectures 5 and 6 that continue lecture notes [20]. Content of Lectures 1–4 of [20] is reviewed for the reader’s convenience in Sections 1–4, respectively. It is shown in Lecture 5 how residual parts of the minimal unitary extensions, that correspond to solutions of the problem, yield some boundary properties of the coefficient matrix-function. These results generalize the classical Nevanlinna–Adamjan–Arov–Kreĭn theorem. Lecture 6 discusses how further properties of the coefficient matrices follow from denseness of certain sets in the associated function model spaces. The structure of the dense set reflects the structure of the problem data.