Carathéodory ‐ Fejér Problem for Pairs of Meromorphic Functions
Daniel Alpay, Vladimir Bolotnikov · Mathematische Nachrichten · 1999
Abstract We continue our study of families of pairs of matrix‐valued meromorphic functions P(ρ,P) depending on two parameters p and P introduced in [2]. These include as special cases the projective Schur, Nevanlinna and Carathéodory classes. A two sided Carathéodory Fejér interpolation problem is defined and solved in P(ρ,P), using the fundamental matrix inequality method. A corresponding Schur algorithm is studied. Finally we also consider the case of functions (as opposed to pairs).