Stable symmetric polynomials and the Schur-Agler class
Complex Variables
2022-03-04 v1 Functional Analysis
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.
Keywords
Cite
@article{arxiv.1008.4560,
title = {Stable symmetric polynomials and the Schur-Agler class},
author = {Greg Knese},
journal= {arXiv preprint arXiv:1008.4560},
year = {2022}
}
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19 pages