Wandering subspaces and the Beurling type theorem, III

Abstract

Let $H^2(D^2)$ be the Hardy space over the bidisk. Let $\{\varphi_n(z)\}_{n \geq 0}$ and $\{\psi_n(w)\}_{n \geq 0}$ be sequences of one variable inner functions satisfying some additinal conditions. Associated with them, we have a Rudin type invariant subspace $\mathcal{M}$ of $H^2(D^2)$. We study the Beurling type theorem for the fringe operator $F_w$ on $\mathcal{M} \ominus z \mathcal{M}$.