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Resonances as viscosity limits for black box perturbations. (English) Zbl 1486.35319

Summary: We show that the complex absorbing potential (CAP) method for computing scattering resonances applies to an abstractly defined class of black box perturbations of the Laplacian in \({{\mathbb{R}}}^n\) which can be analytically extended from \({{\mathbb{R}}}^n\) to a conic neighborhood in \({{\mathbb{C}}}^n\) near infinity. The black box setting allows a unifying treatment of diverse problems ranging from obstacle scattering to scattering on finite volume surfaces.

MSC:

35P25 Scattering theory for PDEs
35B34 Resonance in context of PDEs
35J10 Schrödinger operator, Schrödinger equation
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
47A10 Spectrum, resolvent
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