Two problems on submodules of $H^2({\mathbb{D}}^n)$

Ramlal Debnath, Srijan Sarkar

Given any shift-invariant closed subspace $\mathcal{S}$ (aka submodule) of the Hardy space over the unit polydisc $H^2({\mathbb{D}}^n)$ (where $n\ge 2$), let $R_{z_j}:=M_{z_j}|_{\m…