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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 1992 Volume 203, Pages 21–50 (Mi znsl5770)

This article is cited in 19 papers

Boundary controls and quasiphotons in a Riemannian manifold reconstruction problem via dynamical data

M. I. Belishev, A. P. Katchalov


Abstract: The problem of reconstruction of a Riemannian manifold via it's dynamical Dirichlet to Newmann response operator is considered. The approach for solving the problem is based upon the boundary control theory method. The procedure of reconstruction uses nonstationary Gaussian beams (quasiphotons). The essential feature of the procedure is locality. The class of manifolds which may be reconstructed by this approach is described in terms of the boundary control theory. It includes for instance all analitical manifolds.

UDC: 517.946


 English version:
Journal of Mathematical Sciences, 1996, 79:4, 1172–1190

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