2 problems

Let ${\rm {\mathcal{D}}}$ denote the classical Dirichlet space, let $f\in {\rm {\mathcal{D}}}$ be outer, and let $\mathcal{Z}(f)$ be its boundary zero set. Writing $c_m$ for the ca…

Let $\omega$ be a positive superharmonic weight on $\mathbb{D}$, and let $f\in\mathcal{D}_\omega$. Write $[f]_{\mathcal{D}_\omega}$ for the smallest closed shift-invariant subspace…