Blaschke sequences and zero sets for Dirichlet spaces with superharmonic weights

Using Newtonian potentials and balayages of positive Borel measures, we describe the family of superharmonically weighted Dirichlet spaces D omega\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {D}_\omega $$\end{document} for which every Blaschke sequence is a zero set. We also investigate random zero sets and random Blaschke products in D omega\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {D}_\omega $$\end{document} spaces.