Classes of pairs of meromorphic matrix valued functions generated by nonnegative kernels and associated Nevanlinna-Pick problems

Abstract

Families of pairs of matrix-valued meromorphic functions $$\mathcal{P}$$ (ρ,P) depending on two parameters ϱ andP are introduced. They are the projective analogues of classes of functions studied in [1] and include as special cases the projective Schur, Nevanlinna and Caratheodory classes. A two sided Nevanlinna-Pick interpolation problem is defined and solved in $$\mathcal{P}$$ (ρ,P), using the fundamental matrix inequality method.