A multidimensional Borg–Levinson theorem for magnetic Schrödinger operators with partial spectral data

  • Yavar Kian

    Aix-Marseille Université, Marseille, France

Abstract

We consider the multidimensional Borg–Levinson theorem of determining both the magnetic field and the electric potential , appearing in the Dirichlet realization of the magnetic Schrödinger operator on a bounded domain , , from partial knowledge of the boundary spectral data of . The full boundary spectral data are given by the set , where is the non-decreasing sequence of eigenvalues of , an associated Hilbertian basis of eigenfunctions and is the unit outward normal vector to . We prove that some asymptotic knowledge of with respect to determines uniquely the magnetic field and the electric potential .

Cite this article

Yavar Kian, A multidimensional Borg–Levinson theorem for magnetic Schrödinger operators with partial spectral data. J. Spectr. Theory 8 (2018), no. 1, pp. 235–269

DOI 10.4171/JST/195