On Schur stable multivariate polynomials

The class of stable multivariate polynomials, recently introduced by Kaczorek (1985), is the largest class of polynomials preserving the stability property under small coefficient variations. The principal goal of the contribution is to show that the class of Schur stable multivariate polynomials is the Moebius transformation of the latter one. This fundamental relation provides a vehicle to translate results known for one class to the other one.