DETERMINATION OF THE DENSITY DISTRIBUTION OF A VIBRATING BODY

We give a simple proof for a uniqueness theorem of a multidimensional inverse eigenvalue problem. It consists in the determination of the de nsity distribution of a vibrating body from the knowledge of the eigen values and the traces of eigenfunctions on the boundary of the body. I n the Neumann eigenvalue problem considered here the boundary informat ion, which corresponds to the zero eigenvalue, consists in the gravita tional potential.