On interpolation in Carath\'eodory hyperbolic domains

TL;DR

This paper investigates the relationship between Pick bodies in Carathéodory hyperbolic domains and contractions in finite-dimensional Hilbert spaces, providing conditions for representing these bodies within the unit disc.

Contribution

It introduces a sufficient condition for realizing Pick bodies on Carathéodory hyperbolic domains as those on the open unit disc.

Findings

Established a link between Pick bodies and Hilbert space contractions.

Provided a criterion for embedding Pick bodies into the unit disc.

Enhanced understanding of interpolation in hyperbolic domains.

Abstract

We study the relation between Pick bodies on Carath\'eodory hyperbolic domains and contractions on finite dimensional Hilbert spaces. We give a condition sufficient to realize Pick bodies on Carath\'eodory hyperbolic domains as a Pick body on the open unit disc.