Generic simplicity of resonances in obstacle scattering

Abstract

We show that all resonances in Dirichlet obstacle scattering (in C \mathbb {C} in odd dimensions and in the logarithmic cover of C ∖ { 0 } \mathbb {C}\setminus \{0\} in even dimensions) are generically simple in the class of obstacles with C k C^k (and C ∞ C^\infty ) boundaries, k ≥ 2 k \geq 2 . The method also yields a Hadamard type variational formula for a simple resonance.