An Inverse Eigenvalue Problem of Order Four

In this paper coefficients A(s) ∈ c^∞ [0,1], B(s) ∈ c^∞ [0,1] are constructed so that given positive numbers λ ₁ < λ ₂ < ⋯ < λ ₙ, are the first n eigenvalues and given positive numbers ρ ₁ , ⋯ ,ρ ₙ are the first n normalization constants for the first n eigenfunctions for the fourth order self-adjoint eigenvalue problem y⁽⁴⁾ + (Ay⁽¹⁾ )⁽¹⁾ + By - λ y = 0, y(0) = y⁽¹⁾ (0) = y(1) = y⁽¹⁾ (1) = 0. The solution is determined from the spectral function for the eigenvalue problem.