Polynomials defining distinguished varieties

Greg Knese

doi:10.1090/S0002-9947-2010-05275-4

Polynomials defining distinguished varieties

Greg Knese

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

38 Scopus citations

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 formula 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.

Original language	English
Pages (from-to)	5635-5655
Number of pages	21
Journal	Transactions of the American Mathematical Society
Volume	362
Issue number	11
DOIs	https://doi.org/10.1090/S0002-9947-2010-05275-4
State	Published - Nov 2010

Keywords

Bidisk
Distinguished varieties
Stable polynomials

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10.1090/S0002-9947-2010-05275-4

Cite this

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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 formula 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.",

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AB - 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 formula 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.

KW - Bidisk

KW - Distinguished varieties

KW - Stable polynomials

UR - https://www.scopus.com/pages/publications/78149265184

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 11

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Polynomials defining distinguished varieties

Abstract

Keywords

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