Abstract
The inverse spectral problem of recovering density in a bounded domain is considered. The first N eigenvalues and traces on the boundary of the normal derivatives of the eigenfunctions of the Dirichlet problem are considered as the input data. It is shown that the error of the density recovery does not exceed cln−Β N, where c and Β are certain positive constants.
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References
J. L. Lions and E. Magenes,Inhomogeneous Boundary-Value Problems and Their Applications, Vol. 1 [Russian translation], Mir, Moscow (1971).
I. K. Daugavet,Introduction to the Theory of Approximation of Functions [in Russian], Leningrad Univ. Press, Leningrad (1977).
Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 239, 1997, pp. 218–224.
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Starkov, A.S. On recovering density in a plane domain from incomplete spectral data. J Math Sci 96, 3419–3422 (1999). https://doi.org/10.1007/BF02172820
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DOI: https://doi.org/10.1007/BF02172820