Polynomials defining distinguished varieties

Abstract

Using a sums of squares formula for two variable polynomials with no zeros on the bidisk, we are able to give a new proof of a representation for distinguished varieties. For distinguished varieties with no singularities on the two-torus, we are able to provide extra details about the representation formula and use this to prove a bounded extension theorem.

26 pages

References in corpus (3)

• Bernstein-Szegő measures on the two dimensional torus
• Function theory on the Neil parabola
• A Constrained Nevanlinna-Pick Interpolation Problem

Cited by in corpus (16)

• Polynomials with no zeros on the bidisk
• Nevanlinna-Pick interpolation on distinguished varieties in the bidisk
• Distinguished Varieties Through the Berger--Coburn--Lebow Theorem
• Kummert's approach to realization on the bidisk
• Integrability and regularity of rational functions
• Algebraic pairs of isometries
• Polynomials with no zeros on a face of the bidisk
• Level curve portraits of rational inner functions
• Fejér-Riesz factorizations and the structure of bivariate polynomials orthogonal on the bi-circle
• Determinantal representations of semi-hyperbolic polynomials
• Extreme points and saturated polynomials
• The wedge-of-the-edge theorem: edge-of-the-wedge type phenomenon within the common real boundary
• Traces of analytic uniform algebras on subvarieties and test collections
• Shift-cyclicity in analytic function spaces
• Finite Rank Isopairs
• What Hilbert spaces can tell us about bounded functions on the bidisk