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Spectral Problems in Inverse Scattering Theory
Fioralba Cakoni, Rutgers University
Location: Hill 705
Date & time: Tuesday, 27 February 2018 at 1:40PM - 2:40PM
Abstract: The inverse scattering problem for inhomogeneous media amounts to inverting a locally compact nonlinear mapping, thus presenting severe problems in arriving at a solution. A possible approach to this problem is to exploit spectral properties of operators associated with scattering phenomena which carry essential information about the media. The identified set of eigenvalues must satisfy two important properties:
1) it can be determined from the scattering data
2) it is related to geometrical and physical properties of the media in an understandable way.
In this talk we will discuss some old and new eigenvalue problems arising in scattering theory for inhomogeneous media. We will present a two-fold analysis: on one hand relating the eigenvalues to the scattering operator (to address the first property) and on the other hand viewing them as the spectrum of appropriate (possibly non-self-adjoint) partial differential operators (to address the second property).