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Schur-Agler class rational inner functions on the tridisk


Author: Greg Knese
Journal: Proc. Amer. Math. Soc. 139 (2011), 4063-4072
MSC (2010): Primary 47A57; Secondary 42B05
DOI: https://doi.org/10.1090/S0002-9939-2011-10975-4
Published electronically: March 30, 2011
MathSciNet review: 2823051
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Abstract: We prove two results with regard to rational inner functions in the Schur-Agler class of the tridisk. Every rational inner function of degree $ (n,1,1)$ is in the Schur-Agler class, and every rational inner function of degree $ (n,m,1)$ is in the Schur-Agler class after multiplication by a monomial of sufficiently high degree.


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Additional Information

Greg Knese
Affiliation: Department of Mathematics, Box 870350, University of Alabama, Tuscaloosa, Alabama 35487-0350
Email: geknese@bama.ua.edu

DOI: https://doi.org/10.1090/S0002-9939-2011-10975-4
Keywords: Schur-Agler class, von Neumann’s inequality, bidisk, polydisk, rational inner function, trigonometric polynomials, sums of squares
Received by editor(s): October 5, 2010
Published electronically: March 30, 2011
Additional Notes: This research was supported by NSF grant DMS-1048775
Communicated by: Richard Rochberg
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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