Yixin Yang, Senhua Zhu, Yufeng Lu. Source: Annals of Functional Analysis, Volume 10, Number 4, 447--459.Abstract:
In this paper, we show that, for the rational inner function $\theta (z,w)=\frac{zw+\overline{b}w+\overline{c}z+\overline{d}}{1+bz+cw+dzw}$ , $S_{z}$ is reducible on the quotient module $\mathcal{K}_{\theta }=H^{2}\ominus \theta H^{2}$ over the bidisk if and only if $\theta $ is the product of two one-variable inner functions.