Geodesic
On a perturbation of the poles of scattering matrix for varying baundary condition
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 12, Tome 117 (1981), pp. 183-191 
S. V. Petras. On a perturbation of the poles of scattering matrix for varying baundary condition. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 12, Tome 117 (1981), pp. 183-191. http://geodesic.mathdoc.fr/item/ZNSL_1981_117_a12/
@article{ZNSL_1981_117_a12,
     author = {S. V. Petras},
     title = {On a perturbation of the poles of scattering matrix for varying baundary condition},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {183--191},
     year = {1981},
     volume = {117},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1981_117_a12/}
}
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TI  - On a perturbation of the poles of scattering matrix for varying baundary condition
JO  - Zapiski Nauchnykh Seminarov POMI
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VL  - 117
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1981_117_a12/
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ID  - ZNSL_1981_117_a12
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%A S. V. Petras
%T On a perturbation of the poles of scattering matrix for varying baundary condition
%J Zapiski Nauchnykh Seminarov POMI
%D 1981
%P 183-191
%V 117
%U http://geodesic.mathdoc.fr/item/ZNSL_1981_117_a12/
%G ru
%F ZNSL_1981_117_a12

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

It is considered the behavior of the poles $z_n(\varepsilon)$, $n=1,2,\dots$ of scattering matrix of the operator $l_\varepsilon u=-\Delta u(x), x\in\Omega, \displaystyle\varepsilon\frac{\partial u}{\partial n}+\sigma(x)u|_{\partial\Omega}$ for $\varepsilon\to0$. It is proved that $|z_n(\varepsilon)-z_n|=O(\varepsilon^{\frac1{2q_n}})$ where $q_n$ is the order of pole $z_n$ of scattering matrix of the operator $l_0u=-\Delta u, u|_{\partial\Omega}=0$.