Abstract
Let M be a manifold with boundary δM≠Ф. Let A be a second-order elliptic partial differential operator given on M. Denote by Rλ(x, y), x, y∈M, λε\(\mathbb{C}\)\σ(A) the Schwartz kernel of (A−λI)−1. Consider the Gel'fand inverse boundary problem of the reconstruction of (M, A) via a given Rλ(x, y), x, y∈δM,λε\(\mathbb{C}\). We prove that if the principal symbol of A satisfies some geometric condition (the Bardos-Lebeau-Rauch condition), then these data determine M uniquely, and they determine A to within the group of generalized gauge transformation on M. The above-mentioned geometric condition means, roughly speaking, that any geodesic (in the metric generated by A) leaves M. Bibliography: 29 titles.
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Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 250, 1998, pp. 161–190.
Translated by Ya. Kurylev.
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Kurylev, Y.V., Lassas, M. Abel-Lidskii bases in the non-self-adjoint inverse boundary problem. J Math Sci 102, 4237–4257 (2000). https://doi.org/10.1007/BF02673855
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DOI: https://doi.org/10.1007/BF02673855