Title
Hölder stability of an inverse spectral problem for a magnetic Schrödinger operator on a simple manifold
Abstract
In this talk I will show that on a simple Riemannian manifold a non-negative electric potential and the solenoidal part of a magnetic potential can be recovered Hölder stably from the boundary spectral data of a Magnetic Schrödinger operator. This data contains eigenvalues and Neumann traces of the corresponding sequence of Dirichlet eigenfunctions of the operator. Our proof contains two parts, which I present in the reverse order. 1) We show that the boundary spectral data can be stably obtained from the hyperbolic Dirichlet-to-Neumann map associated with the respective initial / boundary value problem for a hyperbolic equation, whose leading order terms are a priori known. 2) We construct geometric optics solutions to the hyperbolic equation which reduce the stable recovery of the lower order terms to the stable inversion of the geodesic X-ray transform.
This talk is based on an ongoing work with: Boya Liu (North Dakota State U.), Hadrian Quan (U. of California Santa Barbara) and Lili Yan (University of Minnesota)
