Random inverse spectral problems and closed random exponential systems

Abstract

We study the inverse eigenvalue problem for the half-line random Schrödinger operators. Generalizing results from Miklòs Horvàth, we obtain optimal and almost optimal conditions for a set of eigenvalues to determine the random Schrödinger operator almost precisely. These conditions are simple closed properties of the random exponential system corresponding to the known eigenvalues.

On completeness of root vectors of Schrodinger operators: a spectral approach

“…The completeness of the eigenmodes of a grounded parallel plate waveguide is given in [10], whose proof is based on a general theorem governing the completeness of sets of complex exponentials, which is similar to the complex-analytic approach to [18,20] and [19].…”

“…Inspired by [2], in this paper, we will investigate the completeness of root vector systems associated to Schrödinger operators by spectral conditions rather than boundary conditions. Our proof is based on the complex-analytic approach which is similar to [10,18,20] and [19]. More accurately, we will consider PDE of the form…”