We discuss several important open problems of Function Theory, Operator Theory, and Approximation Theory related to the notion of the Nevanlinna domain. These are the domains of the complex plane such that the conjugated identity function on their boundary admits a meromorphic bounded type extension inside the domain. The problems under consideration include those of boundary regularity of Nevanlinna domains and the relations between Nevanlinna domains, quadrature domains, and the Model subspaces of the Hardy space. Other related objects are Beurling inner functions with support on the Beurling-Carleson sets appearing in the recent result of Dyakonov- Khavinson on smooth functions in the Model subspaces, the Brennan conjecture in conformal mapping, and the univalent functions in the Paley-Wiener space.

Participants

Anton Baranov (St. Petersburg State University)
Alexander Borichev (Aix-Marseille Université)
Konstantin Fedorovskiy (Bauman Moscow State Technical University)

Sponsor