Interpolation and sampling for analytic selfmappings of the disc

Abstract

Two different problems are considered here. First, a version of Schwarz-Pick Lemma for $n$ points leads to an interpolation problem for analytic functions from the disc into itself, which may be considered as a particular case of the classical Nevanlinna-Pick interpolation problem. Second, a characterization of sampling sequences for this class of functions is given.

21 pages