@inbook{effbf974ad224f6f9b0c9d0e05706829,

title = "Rational inner functions on a square-matrix polyball",

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 a multiple of 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{\textquoteright}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.",

author = "Anatolii Grinshpan and Kaliuzhnyi-Verbovetskyi, {Dmitry S.} and Victor Vinnikov and Woerdeman, {Hugo J.}",

note = "Funding Information: AG, DK-V, HW were partially supported by NSF grant DMS-0901628. DK-V and VV were partially supported by BSF grant 2010432. Publisher Copyright: {\textcopyright} The Author(s) and the Association for Women in Mathematics 2017.",

year = "2017",

month = jan,

day = "1",

doi = "10.1007/978-3-319-51593-9_10",

language = "English",

series = "Association for Women in Mathematics Series",

publisher = "Springer",

pages = "267--277",

booktitle = "Association for Women in Mathematics Series",

address = "Germany",

}