Quid of Cyclicity in Spaces of Holomorphic Functions of Several Variables

par M. Pouriya Torkinejad Ziarati (Institute de Mathematiques de Toulouse)

mercredi 14 oct. 2026, 18:00 → 19:30 Europe/Paris

1R2 207 (Salle Pellos)

Consider a Hilbert space of holomorphic functions on a domain in (\mathbb{C}^n). A function in this space is called cyclic if the linear span of its polynomial multiples is dense in the space. Determining whether a function is cyclic depends heavily on the space under consideration. An important factor is the zero set of the function. In particular, while zeros inside the domain typically prevent cyclicity, the role of boundary zeros is more subtle.

In this talk, we first introduce the notion of cyclicity through classical Hardy and Dirichlet spaces of the unit disk. We then turn to Dirichlet-type spaces on the unit ball and the bidisk. Our main goal is to discuss how the geometry and dimension of the boundary zero sets affect cyclicity. To this end, we present some recent results and examples illustrating the connection between cyclicity and the geometry of zero sets.