A Refined Schwarz Lemma for the Spectral Nevanlinna-Pick Problem

摘要

The spectral Nevanlinna-Pick problem asks for necessary and sufficient conditions for the existence of a holomorphic map from the unit disc to the set of n × n complex matrices with spectral radius less than 1, that interpolates given data. Some versions of the Schwarz lemma, obtained by Ransford and Nokrane, and by Bharali, provide necessary conditions. We prove a refined version of their results, which makes it possible to treat problems with more than two interpolation points.