A new approach to the 2-variable Subnormal Completion Problem

Authors

• Raúl E. Curto, University of Iowa
• Sang Hoon Lee, Chungnam National University
• Jasang Yoon, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

10-1-2010

Abstract

We study the Subnormal Completion Problem (SCP) for 2-variable weighted shifts. We use tools and techniques from the theory of truncated moment problems to give a general strategy to solve SCP. We then show that when all quadratic moments are known (equivalently, when the initial segment of weights consists of five independent data points), the natural necessary conditions for the existence of a subnormal completion are also sufficient. To calculate explicitly the associated Berger measure, we compute the algebraic variety of the associated truncated moment problem; it turns out that this algebraic variety is precisely the support of the Berger measure of the subnormal completion.

Comments

© 2010 Elsevier Inc. http://www.elsevier.com/open-access/userlicense/1.0/

Recommended Citation

Curto, Raúl E., Sang Hoon Lee, and Jasang Yoon. "A new approach to the 2-variable subnormal completion problem." Journal of mathematical analysis and applications 370, no. 1 (2010): 270-283. https://doi.org/10.1016/j.jmaa.2010.04.061

First Page

270

Last Page

283

Publication Title

Journal of Mathematical Analysis and Applications

DOI

10.1016/j.jmaa.2010.04.061