Finite-dimensional spectral inverse problem for the bundle of Hermite quadratic forms

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.