Geodesic
To the Kac problem of a reconstruction of the area shape by the spectrum of the Dirichlet problem
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 18, Tome 173 (1988), pp. 30-41

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The inverse problem of M. Kac is considered. The procedure of a reconstruction of a area shape is described for the wide class of convex areas. This result can be generalized on some classes of nonconvex areas. 
@article{ZNSL_1988_173_a2,
     author = {M. I. Belishev},
     title = {To the {Kac} problem of a reconstruction of the area shape by the spectrum of the {Dirichlet} problem},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {30--41},
     publisher = {mathdoc},
     volume = {173},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1988_173_a2/}
}
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M. I. Belishev. To the Kac problem of a reconstruction of the area shape by the spectrum of the Dirichlet problem. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 18, Tome 173 (1988), pp. 30-41. http://geodesic.mathdoc.fr/item/ZNSL_1988_173_a2/