Nevanlinna-Pick problem and uniqueness of left inverses in convex domains, symmetrized bidisc and tetrablock

TL;DR

This paper investigates the conditions under which left inverses solving the two-point Nevanlinna-Pick problem are unique across various complex domains, including convex, strongly linearly convex, symmetrized bidisc, and tetrablock.

Contribution

It provides new insights into the uniqueness of solutions to the Nevanlinna-Pick problem in these specific complex domains.

Findings

Uniqueness criteria established for convex domains

Results extend to strongly linearly convex domains

Analysis includes symmetrized bidisc and tetrablock

Abstract

In the paper we discuss the problem of uniqueness of left inverses (solutions of two point Nevanlinna-Pick problem) in bounded convex domains, strongly linearly convex domains, the symmetrized bidisc and the tetrablock.