T. J. Christiansen
Published 2008-01-04Version 1
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.
On the resonances of the Laplacian on waveguides
Singularities and asymptotic distribution of resonances for Schrödinger operators in one dimension
Lower bounds for resonance counting functions for obstacle scattering in even dimensions
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