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Surface waves and scattering by unbounded obstacles

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Periodic and Ergodic Spectral Problems

Consider the Laplace operator $H=-Delta$ in the exterior $Omega$ of a parabolic region in ${f R}d$, and let $H_{0}=-Delta$ be the operator in the space $L2 ({f R}^d)$. The wave operators for the pair $H_{0}$, $H$ exist for an arbitrary self-adjoint boundary condition on $partialOmega$. For the case of the Dirichlet boundary condition, the wave operators are unitary which excludes the existence of surface waves on $partialOmega$. For the Neumann boundary condition, the existence of surface waves is an open problem, and we are going to discuss it.

This talk is part of the Isaac Newton Institute Seminar Series series.

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