Two-Sided Nevanlinna-Pick Interpolation for a Class of Matrix-Valued Functions

Abstract

Families of Matrix-valued analytic functions $W(\rho ,P)$ depending on two parameters $\rho$ and $P$ are introduced. These include as special cases the Schur and Carathéodory functions, as well as classes of functions studied by the authors in [1] and by D. Alpay and H. Dym in [6]. A two sided Nevanlinna-Pick interpolation problem is defined and solved in $W(\rho ,P)$, using the fundamental matrix inequality method.