Abstract
We study the spectral problem
$$\left. {\Delta \mathcal{U} + K^2 \mathcal{U} = 0, \frac{{\partial u}}{{\partial n}} - iK\mathcal{O}\mathcal{U}} \right|_{\partial \Omega } = 0, \mathfrak{S} \geqslant 0$$
We construct a self-adjoint dilatation and the problem is reduced to the investigation of a dissipative operator in a space with energy metric.
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Literature cited
P. D. Lax and R. S. Phillips, J. Funct. Anal.,14, 172–235 (1973).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 73, pp. 217–223, 1977.
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Pavlov, B.S., Faddeev, M.D. Construction of a self-adjoint dilatation for a problem with impedance boundary condition. J Math Sci 34, 2152–2156 (1986). https://doi.org/10.1007/BF01741592
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DOI: https://doi.org/10.1007/BF01741592