Stability estimate for a multidimensional inverse spectral problem with partial spectral data |
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Authors: | Mourad Bellassoued Masahiro Yamamoto |
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Affiliation: | a Faculté des Sciences de Bizerte, Département des Mathématiques, 7021 Jarzouna Bizerte, Tunisia b Laboratoire LMAM, UMR 7122, Université de Paul Verlaine-Metz et CNRS, Ile du Saulcy, 57045 Metz cedex, France c Department of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153, Japan |
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Abstract: | In Bellassoued, Choulli and Yamamoto (2009) 4] we proved a log-log type stability estimate for a multidimensional inverse spectral problem with partial spectral data for a Schrödinger operator, provided that the potential is known in a small neighbourhood of the boundary of the domain. In the present paper we discuss the same inverse problem. We show a log type stability estimate under an additional condition on potentials in terms of their X-ray transform. In proving our result, we follow the same method as in Alessandrini and Sylvester (1990) 1] and Bellassoued, Choulli and Yamamoto (2009) 4]. That is we relate the stability estimate for our inverse spectral problem to a stability estimate for an inverse problem consisting in the determination of the potential in a wave equation from a local Dirichlet to Neumann map (DN map in short). |
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Keywords: | Wave equation Inverse spectral problem X-ray transform DN map |
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