Illinois Journal of Mathematics

Stable symmetric polynomials and the Schur–Agler class

Greg Knese

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Abstract

We call a multivariable polynomial an Agler denominator if it is the denominator of a rational inner function in the Schur–Agler class, an important subclass of the bounded analytic functions on the polydisk. We give a necessary and sufficient condition for a multi-affine, symmetric, and stable polynomial to be an Agler denominator and prove several consequences. We also sharpen a result due to Kummert related to three variable, multi-affine, stable polynomials.

Article information

Source
Illinois J. Math., Volume 55, Number 4 (2011), 1603-1620.

Dates
First available in Project Euclid: 12 July 2013

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1373636698

Digital Object Identifier
doi:10.1215/ijm/1373636698

Mathematical Reviews number (MathSciNet)
MR3082883

Zentralblatt MATH identifier
1278.47024

Subjects
Primary: 47A57: Operator methods in interpolation, moment and extension problems [See also 30E05, 42A70, 42A82, 44A60]
Secondary: 30C15: Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral) {For algebraic theory, see 12D10; for real methods, see 26C10} 42B05: Fourier series and coefficients

Citation

Knese, Greg. Stable symmetric polynomials and the Schur–Agler class. Illinois J. Math. 55 (2011), no. 4, 1603--1620. doi:10.1215/ijm/1373636698. https://projecteuclid.org/euclid.ijm/1373636698


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