Finite dimensional spectral inverse problem for a bundle of hermitian quadratic forms

Abstract

The paper is devoted to recovering the coefficients of a pair of Hermitian quadratic forms c(x, x) and (x, x) in a special basis, in which the matrix of the form c(x, x) is tridiagonal and the matrix of the form m(x, x) is diagonal. The form c(x, x) is positive definite, and the form m(x, x) is nondegenerate, but is not positive difinite in contrast with a well-known case. The data of the inverse problem include the spectrum λ₁...,λ_n of the bundle II_λ and the set of numbers ρ₁...,ρ_n connected with the main normalized elements of the bundle. A procedure for solving the inverse problem is described. The characteristic conditions for λ₁...,λ_n; are found that provide its solution. Bibliography: 5 titles.