On bounded holomorphic interpolation in several variables

Abstract

We show how the reproducing kernel Hilbert space approach to some holomorphic interpolation problems can be utilized to proveboundedness of their solutions. The goal is two-fold: i) to propose a several variable analogue of the classical Pick-Nevanlinna theorem, ii) to display that a simple argumentation may be carried on in this case, which, though still in a Hilbert space context, avoids any use of operator theory.