Resonances sets of Schrödinger operators

by Pavel Gubkin (Univesity of Bonn)

Friday Oct 30, 2026, 2:15 PM → 3:15 PM Europe/Berlin

Endenicher Allee 60, Seminarraum 0.011 (Mathezentrum)

Resonances of Schrödinger operator $\mathcal{H}_q u = -u'' + qu$ are zeroes of the corresponding entire Jost function with negative imaginary part. Resonances play an important role in the spectral theory, in particular, they determine the potential $q$ of the operator uniquely up to the finite number of bound states.

For a discrete set $\Lambda$ of points in the complex plane define its Poisson density as
$$
P_{\Lambda}(x) = \sum_{z\in \Lambda} \frac{|\Im z|}{|z - x|^2}.
$$
In the talk we will characterize resonances sets in terms of the Poisson density and prove that, for every set $\Lambda$  with  uniformly bounded density $P_{\Lambda}$, there exists a potential whose resonance set contains $\Lambda$. The talk is based on the ongoing work with Yurii Belov.