The asymptotic of spectrum of the Maxwell's operator.

Yu. G. Safarov

Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 15, Tome 127 (1983), pp. 169-180

Résumé

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 $N^\pm(\lambda)=(3\pi^2)^{-1}\operatorname{mes}\Omega\cdot\lambda^3+O(\lambda^2)$.