Geometrization of Rings as a Method for Solving Inverse Problems
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.
KeywordsInverse Problem Riemannian Manifold Riemann Surface Operator Algebra Boundary Control
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