Starkov, A. S. On recovering density in a plane domain from incomplete spectral data. (English. Russian original) Zbl 0934.35208 J. Math. Sci., New York 96, No. 4, 3419-3422 (1999); translation from Zap. Nauchn. Semin. POMI 239, 218-224 (1997). Summary: 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 \(c\ln^{-\beta}N\), where \(c\) and \(\beta\) are certain positive constants. MSC: 35R30 Inverse problems for PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 35P05 General topics in linear spectral theory for PDEs Keywords:Helmholtz equation; harmonic function; inverse spectral problem; bounded domain; eigenvalues; eigenfunctions; Dirichlet problem × Cite Format Result Cite Review PDF Full Text: DOI References: [1] J. L. Lions and E. Magenes,Inhomogeneous Boundary-Value Problems and Their Applications, Vol. 1 [Russian translation], Mir, Moscow (1971). · Zbl 0212.43801 [2] I. K. Daugavet,Introduction to the Theory of Approximation of Functions [in Russian], Leningrad Univ. Press, Leningrad (1977). · Zbl 0414.41001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.