Year of Publication
Doctor of Philosophy (PhD)
Arts and Sciences
Dr. Russell Brown
We consider the inverse problem for the magnetic Schrödinger operator with the assumption that the magnetic potential is in Cλ and the electric potential is of the form p1 + div p2 with p1, p2 ∈ Cλ. We use semiclassical pseudodifferential operators on semiclassical Sobolev spaces and Bourgain type spaces. The Bourgain type spaces are defined using the symbol of the operator h2Δ + hμ ⋅ D. Our main result gives a procedure for recovering the curl of the magnetic field and the electric potential from the Dirichlet to Neumann map. Our results are in dimension three and higher.
Digital Object Identifier (DOI)
Zhang, Yaowei, "The Bourgain Spaces and Recovery of Magnetic and Electric Potentials of Schrödinger Operators" (2016). Theses and Dissertations--Mathematics. 41.