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Erschienen in:
2009 | OriginalPaper | Buchkapitel
Geometrization of Rings as a Method for Solving Inverse Problems
verfasst von : Mikhail Belishev
Erschienen in: Sobolev Spaces in Mathematics III
Verlag: Springer New York
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In the boundary value inverse problems on manifolds, it is required to recover a Riemannian manifold ʊ from its boundary inverse data (the elliptic or hyperbolic Dirichlet-to-Neumann map, spectral data, etc). We show that for a class of elliptic and hyperbolic problems the required manifold is identical with the spectrum of a certain algebra determined by the inverse data and, consequently, to recover the manifold it suffices to represent the corresponding algebra in the relevant canonical form.