Abstract
For the distribution functions of the positive and the negative eigenvalues of the operator
in a domain Ω with a smooth boundary, one obtains the asymptotic formula N±(λ)=(3π2)−1 mes Ω·λ3+0(λ2). Under additional assumptions on the properties of the geodesic billiard in Ω, one shows that N±(λ)= (3π2)−1 mes Ω·λ3+0(λ2).
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 127, pp. 169–180, 1983.
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Safarov, Y.G. Asymptotic behavior of the spectrum of the Maxwell operator. J Math Sci 27, 2655–2661 (1984). https://doi.org/10.1007/BF01103726
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DOI: https://doi.org/10.1007/BF01103726