This article is cited in 2 scientific papers (total in 2 papers)
Noncommutative geometry and the tomography of manifolds
M. I. Belishevab, M. N. Demchenkoab, A. N. Popova
a Saint Petersburg State University
b St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences
The tomography of manifolds describes a range of inverse problems in which we seek to reconstruct a Riemannian manifold from its boundary data (the “Dirichlet–Neumann” mapping, the reaction operator, and others). Different types of data correspond to physically different situations: the manifold is probed by electric currents or by acoustic or electromagnetic waves. In our paper we suggest a unified approach to these problems, using the ideas of noncommutative geometry. Within the framework of this approach, the underlying manifold for the reconstruction is obtained as the spectrum of an adequate Banach algebra determined by the boundary data.
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Transactions of the Moscow Mathematical Society, 2014, 75, 133–149
MSC: 35R30, 46L60, 58B34, 93B28, 35Q61
M. I. Belishev, M. N. Demchenko, A. N. Popov, “Noncommutative geometry and the tomography of manifolds”, Tr. Mosk. Mat. Obs., 75, no. 2, MCCME, M., 2014, 159–180; Trans. Moscow Math. Soc., 75 (2014), 133–149
Citation in format AMSBIB
\by M.~I.~Belishev, M.~N.~Demchenko, A.~N.~Popov
\paper Noncommutative geometry and the tomography of manifolds
\serial Tr. Mosk. Mat. Obs.
\jour Trans. Moscow Math. Soc.
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M. I. Belishev, “Boundary control and tomography of Riemannian manifolds (the BC-method)”, Russian Math. Surveys, 72:4 (2017), 581–644
I M. Belishev, V A. Kaplun, “Eikonal algebra on a graph of simple structure”, Eurasian J. Math. Comput. Appl., 6:3 (2018), 4–33
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