Abstract: This is a continuation of last week's talk.
Let $\Omega$ be a planar domain in $\mathbb{C}$. We give necessary and sufficient potential-theoretic conditions for the $\overline{\partial}$-operator to have closed range in $L^{2}(\Omega)$. Moreover, we give a new necessary and sufficient potential-theoretic condition for the Bergman space of a $\Omega$ to be infinite dimensional.
To add/edit talks, please log in on the department web page, then return to Announce. Alternatively if you know the Announce
username/password, click the link below: