Rational inner functions on a square-matrix polyball

Anatolii Grinshpan, Dmitry S. Kaliuzhnyi-Verbovetskyi, Victor Vinnikov, Hugo J. Woerdeman

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

5 Scopus citations


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 a multiple of every polynomial with no zeros in the closed domain is such a denominator. One of our tools is the Korányi–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.

Original languageEnglish
Title of host publicationAssociation for Women in Mathematics Series
Number of pages11
StatePublished - 1 Jan 2017

Publication series

NameAssociation for Women in Mathematics Series
ISSN (Print)2364-5733
ISSN (Electronic)2364-5741

ASJC Scopus subject areas

  • Mathematics (all)
  • Gender Studies


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