Uniqueness for the fractional Calderon problem with quasilocal perturbations

Abstract: We will be talking about the fractional Schrodinger equation with quasilocal perturbations. Quasilocal operators are a special kind of nonlocal operators transforming compactly supported functions into functions of unbounded support with a decay estimate at infinity. These include, among the others, convolutions operators against Schwartz functions. We will show that both qualitative and quantitative unique continuation and Runge approximation properties hold in the assumption of sufficient decay. The results are then used to show uniqueness in the inverse problem of retrieving a quasilocal perturbation from DN data under suitable geometric assumptions. This work generalizes recent results regarding the locally perturbed fractional Calderon problem, and is based on the following paper: arxiv.org/abs/2110.11063

Mathematics

Audience: researchers in the topic

International Zoom Inverse Problems Seminar, UC Irvine