Resolvent at low energy in two dimensions

Tanya Christiansen (U of Missouri, Columbia)

Jul 14. 2023, 09:30 — 10:20

Even for self-adjoint Schr\"odinger operators on $\mathbb{R}^2$, the low energy behavior of the resolvent is rather complicated.  In this talk we look at a new
approach to studying this problem which has the benefit of working for a large class of perturbations of $-\Delta$ on $\mathbb{R}^2$, including some
non-self-adjoint ones.   We obtain asymptotic expansions of the resolvent near $0$ which  have implications for quantities of interest in scattering theory.

This talk is based on joint work with Kiril Datchev.


Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Spectral Theory and Mathematical Relativity (Thematic Programme)
Piotr T. Chruściel (U of Vienna)
Peter Hintz (ETH Zurich)
Alexander Strohmaier (U Leeds)
Steven Morris Zelditch † (Northwestern U Evanston)