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Poisson relation for the scattering kernel and inverse scattering by obstacles. (English) Zbl 0888.58070
The author considers the Dirichlet problem for the wave equation in the exterior of a compact obstacle in $$\mathbb{R}^n,$$ where $$n$$ is odd and $$n\geq 3.$$ It is shown that in a certain class of obstacles, the singularities of the scattering amplitude provide enough information to recover the obstacle. A special case of this result was proved in [V. Petkov and L. Stoyanov, Ann. Inst. H. Poincaré, Phys. Théor. 62, No. 1, 17-45 (1995; Zbl 0838.35093)].
Reviewer: T.Aktosun (Fargo)

##### MSC:
 58J50 Spectral problems; spectral geometry; scattering theory on manifolds 35P25 Scattering theory for PDEs 35Q30 Navier-Stokes equations
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