Frédéric Gaunard: A few words on Interpolation problems in spaces of analytic functions and related topics

In this talk for the Grad Students Seminar, I will introduce the notions of minimality, unicity, interpolation and weak interpolation for a sequence of complex numbers on a Banach space of analytic functions. All those conditions can be reformulated in terms of geometric properties on the associated family of reproducing kernels.

I will present the case of the Hardy Space (of upper half-plane) and the Paley-Wiener Space (for which I will provide definition and some important properties) and state the results.

I will also try to make a link with control theory if there is enough time.