Hampus Nyberg: Deep zero problems and low degree orthogonal polynomials

Abstract:

In this seminar we will discuss two projects.

The first one concerns Deep zero problems which are concerned with large amounts of local information of analytic functions at a small number of distinct points. Here, the analytic functions are restricted to lie in a reproducing kernel Hilbert space. We present a result in the Bargmann–Fock space when the information is distributed 1:2 or 1:3 between two points in an arithmetic fashion.

The second project concerns orthogonal polynomials in the complex plane which can be used to describe charged particles in the plane which are confined by some electrostatic potential. We aim to describe how these polynomials behave as the strength of this potential tends to infinity.