The inside-outside duality in scattering theory
Andreas Kirsch, Karlsruhe Institute of Technology
Viernes 13 de diciembre, ICMAT, aula Azul, 10:00
In this talk I will investigate the relationship between interior eigenvalues of a differential operator and the injectivity of the coresponding far field operator for two scattering problems: In the first one we consider scattering of plane time harmonic waves by an acoustically soft obstacle (that is under Dirichlet boundary conditions). The corresponding interior eigenvalue problem is the classical eigenvalue problem for the Laplacian under Dirichlet boundary conditions. The second one considers the scattering of plane time harmonic waves by an inhomogeneous medium, where the corresponding interior eigenvalue problem consists of an unconvential non-selfadjoint system. The exact equivalence is obtained by a proper weakening of the notion of injectivity.