Polynomials defining distinguished varieties

By Greg Knese. 2009

50 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/84c3df0e974bc8fc3db33429959294c2212da4ea

How researchers see this paper

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In Algebra and Number Theory

1. Greg Knese
2. Jim Agler
3. John E. McCarthy
4. Kelly Bickel

In Computational Theory and Mathematics

1. Greg Knese
2. Kelly Bickel
3. Jim Agler
4. John E. McCarthy
5. Orr Shalit
6. Michael Hartz
7. Joseph A. Ball
8. K. Davidson

In Statistical and Nonlinear Physics

1. John E. McCarthy
2. Jim Agler
3. Kelly Bickel

Citations in the corpus

• Inner functions on the bidisk and associated Hilbert spaces (2012, background): “The details of the canonical spaces and kernels have been important in understanding function theory on distinguished varieties in [21], [20].”
• Pick Interpolation for free holomorphic functions (2013, background): “The geometric conditions that guarantee that all bounded holomorphic functions extend to be bounded on the whole domain have been investigated by Henkin and Polyakov [18] and Knese [20]; however, even when bounded extensions exist, the extension is almost never isometric [1].”