2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145329We 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 $ρ$ does, then the obstacle is a ball of radius $ρ$. We give related results for obstacles which are disjoint unions of several balls of the same radius.Mathematical PhysicsSpectral Theory35P25, 58J50, 35J25text