Inverse spectral theory using nodal points as data—A uniqueness result

The uniqueness theorem for inverse nodal problems with a chemical potential

In this paper, an inverse nodal problem for a second-order differential equation having a chemical potential on a finite interval is investigated. First, we estimate the nodal points and nodal lengths of differential operator. Then, we show that the potential can be uniquely determined by a dense set of nodes of the eigenfunctions.

Inverse uniqueness results for Schrödinger operators using de Branges theory

We utilize the theory of de Branges spaces to show when certain Schrödinger operators with strongly singular potentials are uniquely determined by their associated spectral measure. The results are applied to obtain an inverse uniqueness theorem for perturbed spherical Schrödinger operators.

Uniqueness result for inverse problem of geophysics : I

A uniqueness result is proved for the 3D inverse scattering problem of geophysics with a fixed position of the source and surface data given for all frequencies.

Uniqueness Result for Inverse Problem of Geophysics: I

A Uniqueness Result for the Inverse Transmission Problem

The problem of inverse scattering of a plane acoustic wave by a penetrable scatterer with the transmission boundary condition is studied. It is proved that, if the constant exterior wavenumber is known, then the shape of the obstacle and the constant transmission parameter and the constant interior wavenumber are uniquely determined by the scattering amplitude known at the constant exterior wav...