The PDEs and Applications: Gaussian analytic functions and operator symbols of Dirichlet type

  • Date: –12:15
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
  • Lecturer: Håkan Hedenmalm
  • Organiser: Matematiska institutionen
  • Contact person: Kaj Nyström
  • Seminarium

Abstract: We consider the Gaussian analytic function (GAF) associated with the Dirichlet space of functions vanishing at the origin. We then take two copies of the same GAF, but not necessarily independent. Instead they should have a joint Gaussian structure, with possibly complicated covariance structure. We are interested in the analytic part of this covariance structure.

We show that it is generated by a contraction on L^2 of the disk, and that the analytic covariance function has a finite asymptotic variance. Given that it need not be in the Bloch space,  this does not follow from known results.

We show that the asymptotic variance is at most 2, but it is not clear whether this bound may be reached. An example due to Z. Chase gives that 1.72 may be achieved.