Schur–Nevanlinna–Potapov sequences of rational matrix functions

摘要

We study particular sequences of rational matrix functions with poles outside the unit circle. These Schur–Nevanlinna–Potapov sequences are recursively constructed based on some complex numbers with norm less than one and some strictly contractive matrices. The main theme of this paper is a thorough analysis of the matrix functions belonging to the sequences in question. Essentially, such sequences are closely related to the theory of orthogonal rational matrix functions on the unit circle. As a further crosslink, we explain that the functions belonging to Schur–Nevanlinna–Potapov sequences can be used to describe the solution set of an interpolation problem of Nevanlinna–Pick type for matricial Schur functions.