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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Polynomials defining distinguished varieties


Author: Greg Knese
Journal: Trans. Amer. Math. Soc. 362 (2010), 5635-5655
MSC (2010): Primary 47A57, 47A13, 14M99, 32A10, 32A60, 14H50
Published electronically: June 11, 2010
MathSciNet review: 2661491
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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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Additional Information

Greg Knese
Affiliation: Department of Mathematics, University of California, Irvine, Irvine, California 92614-3875
Address at time of publication: Department of Mathematics, University of Alabama, Box 870350, Tuscaloosa, Alabama 35487-0350
Email: gknese@uci.edu, gknese@bama.ua.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05275-4
PII: S 0002-9947(2010)05275-4
Keywords: Distinguished varieties, stable polynomials, bidisk
Received by editor(s): March 25, 2008
Published electronically: June 11, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.