On a multi-point interpolation problem for generalized Schur functions

Abstract

The nondegenerate Nevanlinna-Pick-Carath\'eodory-Fejer interpolation problem with finitely many interpolation conditions always has infinitely many solutions in a generalized Schur class $\cS_\kappa$ for every $\kappa\ge \kappa_{\rm min}$ where the integer $\kappa_{\rm min}$ equals the number of negative eigenvalues of the Pick matrix associated to the problem and completely determined by interpolation data. A linear fractional description of all $\cS_{\kappa_{\rm min}}$ solutions of the (nondegenerate) problem is well known. In this paper, we present a similar result for an arbitrary $\kappa\ge \kappa_{\rm min}$.