Dominant Sets for Model Spaces in Several Variables

Let \(I\) be an inner function in the domain \(\mathcal{D}=B_{n_1}\times B_{n_2}\times \dots \times B_{n_k}\) , where \(B_n\) is the open unit ball in \(\mathbb{C}^n\) , \(n\ge 1\) . We construct dominant sets for the space \(H^2 \ominus I H^2\) , where \(H^2= H^2(\mathcal{D})\) is the standard Hardy space.