I will present an inverse problem for the fractional Schrödinger equation with a local perturbation by a linear partial differential operator. I will show unique recoverability of the coefficients of the perturbation from the Dirichlet-to-Neumann map associated to the perturbed equation. This is proved for two classes of coefficients: coefficients which belong to certain spaces of Sobolev multipliers and coefficients which belong to fractional Sobolev spaces with bounded derivatives. This study generalizes recent results for the zeroth and first order perturbations to higher order.
This talk is based on recent work of mine with K. Mönkkönen, J. Rallo and G. Uhlmann: https://arxiv.org/abs/2008.10227