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Zapiski Nauchnykh Seminarov LOMI, 1983, Volume 127, Pages 169–180
(Mi znsl4219)
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This article is cited in 4 scientific papers (total in 4 papers)
The asymptotic of spectrum of the Maxwell's operator.
Yu. G. Safarov
Abstract:
The asymptotic formula $N^\pm(\lambda)=(3\pi^2)^{-1}\operatorname{mes}\Omega\cdot\lambda^3+O(\lambda^2)$ is obtained for distribution's functions of positive and negative eigenvalues of the operator $\begin{pmatrix}0 & i\operatorname{rot} \\ -i\operatorname{rot} & 0\end{pmatrix}$ in the domain $\Omega$ with smooth boundary. It is proved under additional assumptions about properties of the geodesic billiards in that $N^\pm(\lambda)=(3\pi^2)^{-1}\operatorname{mes}\Omega\cdot\lambda^3+O(\lambda^2)$.
Citation:
Yu. G. Safarov, “The asymptotic of spectrum of the Maxwell's operator.”, Boundary-value problems of mathematical physics and related problems of function theory. Part 15, Zap. Nauchn. Sem. LOMI, 127, "Nauka", Leningrad. Otdel., Leningrad, 1983, 169–180
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https://www.mathnet.ru/eng/znsl4219 https://www.mathnet.ru/eng/znsl/v127/p169
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Abstract page: | 124 | Full-text PDF : | 60 |
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