Geodesic
Finite-dimensional spectral inverse problem for the bundle of Hermite quadratic forms
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 20, Tome 186 (1990), pp. 33-36

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The paper is devoted to recovering the coefficients of Hermite quadratic forms $c(x,x)$, $m(x,x)$ in the special basis, in which the matrix of $c(x,x)$ is tridiagonal and matrix of $m(x,x)$ is diagonal. The form $c(x,x)$ is positively definited. The form $m(x,x)$ is nondegenerated, but is not positively definite. The inverse problem data consist of the spectrum $\lambda_1,\dots,\lambda_n$ of bundle $\Pi_\lambda(x)=c(x,x)-\lambda m(x,x)$ and the set of numbers $\rho_1,\dots,\rho_n$ connected with the bundle of main normed elements. 
@article{ZNSL_1990_186_a3,
     author = {M. I. Belishev and M. V. Putov},
     title = {Finite-dimensional spectral inverse problem for the bundle of {Hermite} quadratic forms},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {33--36},
     publisher = {mathdoc},
     volume = {186},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1990_186_a3/}
}
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M. I. Belishev; M. V. Putov. Finite-dimensional spectral inverse problem for the bundle of Hermite quadratic forms. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 20, Tome 186 (1990), pp. 33-36. http://geodesic.mathdoc.fr/item/ZNSL_1990_186_a3/