Article
Ufa Mathematical Journal
Volume 4, Number 2, pp. 28-64
Perturbation of an elliptic operator by a narrow potential in $n$-dimensional domain.
Bikmetov A.R., Gadyl'shin R.R.
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We study a discrete spectrum of an elliptic operator of the second order in $n$-dimensional domain, $n\geq 2$, perturbed by a potential depending on two parameters, one of the parameters describes the length of support of the potential and inverse of the other corresponds to the magnitude of the potential. We give the relation between these para\-me\-ters, under which the generalized convergence of the perturbed operator to the unperturbed one holds. Under this relation we construct the asymptotics w.r.t. small parameters of the eigenvalues of perturbed operators.