THE NON-TANGENTIAL BOUNDARY BEHAVIOR OF THE MATRIX-VALUED RATIONAL INNER FUNCTIONS ON BOUNDED SYMMETRIC DOMAIN

Knese [Proc. LMS 111(2015), pp. 1261-1306] proved every rational inner function on polydisc has a non-tangential limit at every point of the Shilov boundary. We extended his result to the case of functions on general bounded symmetric domains. Namely, every rational inner function on a bounded symmetric domain has a non-tangential limit of modulus 1 at every point of the Shilov boundary. We also prove that every matrix-valued rational inner function on tube-type domain has a unitary non-tangential limit at every point of the Shilov boundary.