Abstract
We consider an inverse problem of M. Kac, consisting in the recovery of a domain from the spectrum of a homogeneous Dirichlet boundary value problem. We describe a recovery procedure for a sufficiently broad class of convex domains. The results can be generalized to several classes of nonconvex domains.
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 173, pp. 30–41, 1988.
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Belishev, M.I. A problem of M. Kac concerning recovery of the shape of a domain from the spectrum of a Dirichlet problem. J Math Sci 55, 1663–1672 (1991). https://doi.org/10.1007/BF01098204
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DOI: https://doi.org/10.1007/BF01098204