Geodesic
Indefinite metric and scattering by a~domain with a~small hole
Matematičeskie zametki, Tome 58 (1995) no. 6, pp. 837-850.

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For the problem of plane waves scattered by a domain with a small hole, we suggest a model based on the theory of self-adjoint extensions of symmetric operators in a space with indefinite metric. For two-dimensional problems of scattering on a line with a hole and on a semi-ellipse connected by a hole with a half-plane, we justify the choice of extension that guarantees the coincidence of the model solution with the solution of the “actual” problem in the far zone with a high degree of accuracy. 
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     title = {Indefinite metric and scattering by a~domain with a~small hole},
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A. A. Kiselev; I. Yu. Popov. Indefinite metric and scattering by a~domain with a~small hole. Matematičeskie zametki, Tome 58 (1995) no. 6, pp. 837-850. http://geodesic.mathdoc.fr/item/MZM_1995_58_6_a3/

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