# A new approach to the 2-variable subnormal completion problem - Mathematics > Functional Analysis

A new approach to the 2-variable subnormal completion problem - Mathematics > Functional Analysis - Download this document for free, or read online. Document in PDF available to download.

Abstract: We study the Subnormal Completion Problem SCP for 2-variable weightedshifts. We use tools and techniques from the theory of truncated momentproblems to give a general strategy to solve SCP. We then show that when allquadratic moments are known equivalently, when the initial segment of weightsconsists of five independent data points, the natural necessary conditions forthe existence of a subnormal completion are also sufficient. To calculateexplicitly the associated Berger measure, we compute the algebraic variety ofthe associated truncated moment problem; it turns out that this algebraicvariety is precisely the support of the Berger measure of the subnormalcompletion.

Author: ** Raul E. Curto, Sang Hoon Lee, Jasang Yoon**

Source: https://arxiv.org/