Infinitely supported harmonically weighted Dirichlet spaces which are de Branges Rovnyak spaces

In this talk, we discuss when de Branges-Rovnyak spaces $H(b)$ are also harmonically weighted Dirichlet spaces $\mathcal{D}_\mu$. In particular, we focus on the case where $\mu$ is an atomic measure with infinitely many atoms, i.e., it has the form

$µ=\sum_{n=0}^\infty \alpha_n \delta_{\zeta_n},$

with $\zeta_n \in \partial D$ and $\alpha_n\gt 0$ such that $(a_n) \in \ell^1(\mathbb{N})$.

This is based on a joint work with Carlo Bellavita, Andreas Hartmann and Javad Mashreghi (see the preprint on HAL).