Geodesic
On recovering of the density in the plane domain from incomplete spectral data
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 26, Tome 239 (1997), pp. 218-224 Cet article a éte moissonné depuis la source Math-Net.Ru

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An inverse spectral problem of the density recovering is considered. The first $N$ eigenvalues and traces on the boundary of the normal derivatives of eigenfunctions for Dirichlet problem are chosen as input data. The theorem that an error in the density approximation is less than $cN^{-\beta}$, with some positive constants $c$ and $\beta$ is proved. 
@article{ZNSL_1997_239_a17,
     author = {A. S. Starkov},
     title = {On recovering of the density in the plane domain from incomplete spectral data},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {218--224},
     year = {1997},
     volume = {239},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_239_a17/}
}
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A. S. Starkov. On recovering of the density in the plane domain from incomplete spectral data. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 26, Tome 239 (1997), pp. 218-224. http://geodesic.mathdoc.fr/item/ZNSL_1997_239_a17/