On domains of noncommutative rational functions

Abstract

In this paper the stable extended domain of a noncommutative rational function is introduced and it is shown that it can be completely described by a monic linear pencil from the minimal realization of the function. This result amends the singularities theorem of Kalyuzhnyi-Verbovetskyi and Vinnikov. Furthermore, for noncommutative rational functions which are regular at a scalar point it is proved that their domains and stable extended domains coincide.