NON-CYCLICITY AND POLYNOMIALS IN DIRICHLET-TYPE SPACES OF THE UNIT BALL

We give a description of the zero set intersection the unit sphere of a zero-free polynomial in the unit ball of Cn. The nice description leads to the formulation of a conjecture regarding the characterization of polynomials that are cyclic in Dirichlet-type spaces in the unit ball of Cn. Furthermore, we answer partially ascertaining whether an arbitrary polynomial is not cyclic.