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2010 Polynomials with no zeros on the bidisk
Greg Knese
Anal. PDE 3(2): 109-149 (2010). DOI: 10.2140/apde.2010.3.109

Abstract

We prove a detailed sums of squares formula for two-variable polynomials with no zeros on the bidisk D2, extending previous such formulas by Cole and Wermer and by Geronimo and Woerdeman. Our formula is related to the Christoffel–Darboux formula for orthogonal polynomials on the unit circle, but the extension to two variables involves issues of uniqueness in the formula and the study of ideals of two-variable orthogonal polynomials with respect to a positive Borel measure on the torus which may have infinite mass. We present applications to two-variable Fejér–Riesz factorizations, analytic extension theorems for a class of bordered curves called distinguished varieties, and Pick interpolation on the bidisk.

Citation

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Greg Knese. "Polynomials with no zeros on the bidisk." Anal. PDE 3 (2) 109 - 149, 2010. https://doi.org/10.2140/apde.2010.3.109

Information

Received: 23 October 2008; Revised: 20 October 2009; Accepted: 3 December 2009; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1226.42019
MathSciNet: MR2657451
Digital Object Identifier: 10.2140/apde.2010.3.109

Subjects:
Primary: 42C05
Secondary: 14M12, 42B05, 46C07, 47A57

Rights: Copyright © 2010 Mathematical Sciences Publishers

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Vol.3 • No. 2 • 2010
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