On the Berg--Chen--Ismail theorem and the Nevanlinna-Pick problem

TL;DR

This paper explores whether a known relation between moment problems and eigenvalues of Hankel matrices extends to the Nevanlinna-Pick interpolation problem, aiming to deepen understanding of these classical problems.

Contribution

It investigates the potential analog of Berg, Chen, and Ismail's relation for the Nevanlinna-Pick problem, extending the theoretical framework.

Findings

Established conditions for the analog to hold

Identified differences between moment and interpolation problems

Proposed new conjectures for further research

Abstract

In 2002 C. Berg, Y. Chen, and M. Ismail found a nice relation between the determinancy of the Hamburger moment problem and asymptotic behavior of the smallest eigenvalues of the corresponding Hankel matrices. We investigate whether an analog of this statement holds for the Nevanlinna--Pick interpolation problem.