Interpolating Sequences for analytic selfmappings of the disc

TL;DR

This paper explores the interpolation problem for analytic self-mappings of the disc, characterizing interpolating sequences through hyperbolic density, inspired by Schwarz's Lemma.

Contribution

It provides a geometric description of interpolating sequences for self-maps of the disc using hyperbolic density, extending classical results.

Findings

Characterization of interpolating sequences via hyperbolic density

Geometric description of sequences for analytic self-mappings

Extension of Schwarz's Lemma to interpolation problems

Abstract

Schwarz's Lemma leads to a natural interpolation problem for analytic functions from the disc into itself. The corresponding interpolating sequences are geometrically described in terms of a certain hyperbolic density.