On the condensed density of the zeros of the Cauchy transform of a complex atomic random measure with Gaussian moments

TL;DR

This paper studies the distribution of zeros of the Cauchy transform of a complex atomic measure with Gaussian moments, providing an approximation and discussing implications for moments problems.

Contribution

It introduces an approximation for the zeros' distribution of the Cauchy transform of a Gaussian-moment atomic measure, advancing understanding of related moments problems.

Findings

Derived an approximation for the zeros' distribution

Connected zeros distribution to moments problems

Discussed implications for solving moments problems

Abstract

An atomic random complex measure defined on the unit disk with Normally distributed moments is considered. An approximation to the distribution of the zeros of its Cauchy transform is computed. Implications of this result for solving several moments problems are discussed.