Stable symmetric polynomials and the Schur-Agler class

Details Stable symmetric polynomials and the Schur-Agler class Stable symmetric polynomials and the Schur-Agler class

2010-08-26

arxiv.org/abs/1008.4560v1

Mathematics

Complex Variables

19 pages

Scientific paper

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.

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