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Resonances as Viscosity Limits for Black Box Perturbations

Abstract

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.

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Acknowledgements

The author would like to thank Maciej Zworski for helpful discussions. I am also grateful to the anonymous referees for the careful reading of the first version and for many valuable comments. This project was supported in part by the National Science Foundation grant DMS-1901462.

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Correspondence to Haoren Xiong.

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Xiong, H. Resonances as Viscosity Limits for Black Box Perturbations. Ann. Henri Poincaré (2021). https://doi.org/10.1007/s00023-021-01114-4

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