The Calderon Problem for Two-Dimensional Manifolds by the BC-Method
M. I. Belishev
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Source: Crossref
Published: Jan 1, 2003
DOI: 10.1137/s0036141002413919
Open original source ↗Source abstract
As was shown by Lassas and Uhlmann [Ann. Sci. École Norm. Sup. (4), 34 (2001), pp. 771--787], the smooth two-dimensional compact orientable Riemann manifold with the boundary is uniquely determined by its Dirichlet-to-Neumann map (DN-map) up to conformal equivalence. We give a new proof of this fact based on relations between the Calderon problem and function algebras: the manifold is identified with the spectrum of the algebra of holomorphic functions determined by the DN-map up to isometry; as such, the manifold is recovered from the DN-map by the use of the Gelfand transform. A simple formula linking the DN-map to the Euler characteristic of the manifold is derived.
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