Rational inner functions on a square-matrix polyball
Complex Variables
2015-05-21 v1
Abstract
We establish the existence of a finite-dimensional unitary realization for every matrix-valued rational inner function from the Schur--Agler class on a unit square-matrix polyball. In the scalar-valued case, we characterize the denominators of these functions. We also show that every polynomial with no zeros in the closed domain is such a denominator. One of our tools is the Kor\'{a}nyi--Vagi theorem generalizing Rudin's description of rational inner functions to the case of bounded symmetric domains; we provide a short elementary proof of this theorem suitable in our setting.
Cite
@article{arxiv.1505.05437,
title = {Rational inner functions on a square-matrix polyball},
author = {Anatolii Grinshpan and Dmitry S. Kaliuzhnyi-Verbovetskyi and Victor Vinnikov and Hugo J. Woerdeman},
journal= {arXiv preprint arXiv:1505.05437},
year = {2015}
}