Sampling and interpolation for analytic selfmappings of the disc

Abstract

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

20 pages. This is a major revision of the older paper arXiv:1407.7776 especially for the part related to the sampling sequences. There is also a reordering between the two parts