Resonances and balls in obstacle scattering with Neumann boundary conditions

Physics – Mathematical Physics

Scientific paper

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Scientific paper

We consider scattering by an obstacle in $\Real^d$, $d\geq 3 $ odd. We show
that for the Neumann Laplacian if an obstacle has the same resonances as the
ball of radius $\rho$ does, then the obstacle is a ball of radius $\rho$. We
give related results for obstacles which are disjoint unions of several balls
of the same radius.

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