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 $\mathbb{C}^n$, $n\geqslant 1$. 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.