Rational inner functions on a square-matrix polyball Academic Article uri icon

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 Koranyi-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.

publication date

  • January 1, 2017