4 problems

Let $\mathbb{D}^2$ denote the bidisc, and let $\mathfrak{D}(\mathbb{D}^2)=\mathfrak{D}_{(1,1)}(\mathbb{D}^2)$ be the bidisc Dirichlet space. Let $\varphi=\frac{\widetilde{p}}{p}$ b…

Let $\phi$ be a rational inner function on the polydisk $\mathbb{D}^d$, let $\sigma_{\alpha}$ be its Clark measure associated to $\alpha$, and let $\mathcal{C}_{\alpha}(\phi)$ deno…

Let $\phi$ satisfy condition (A1). For $\lambda\in\mathbb{T}$, let $\mathcal{L}_{\lambda}(\phi)$ have $L_{\lambda}$ components near $(1,1)$, and let $\mathcal{Z}_{\tilde{p}}$ have…

Let $\phi$ be a rational inner function, let $\mathcal{Z}_{\tilde{p}}$ denote its relevant zero set, and consider its branches at a singularity on $\mathbb{T}^2$. For generic…