A complete solution to the Cauchy dual subnormality problem for torally expansive toral $3$-isometric weighted $2$-shifts

TL;DR

This paper provides a comprehensive solution to the Cauchy dual subnormality problem for a specific class of weighted 2-shifts, using advanced moment problem techniques related to 2-variable polynomials.

Contribution

It offers a complete characterization of subnormality for torally expansive toral 3-isometric weighted 2-shifts, advancing understanding in operator theory.

Findings

Solved the Cauchy dual subnormality problem for the specified class.

Connected the problem to Hausdorff moment problems in two variables.

Developed new methods involving lower bi-degree polynomial moment problems.

Abstract

In this paper, we present a complete solution to the Cauchy dual subnormality problem for torally expansive toral $3$-isometric weighted $2$-shifts. This solution is obtained by solving a couple of Hausdorff moment problems arising from $2$-variable polynomials of lower bi-degree.