A spectrum determined by eigencurves

This paper investigates the self-adjoint operator -partial derivative(2)/pa rtial derivative x(2) + q(x, y) in the Hilbert space L-2((a, b) x (c, d)) s ubject to the boundary conditions z(a, y) = z(b, y) = 0. It is shown that t he spectrum and spectral representation of A are determined by the eigencur ves and eigenfunctions of the parameterized regular Sturm - Liouville opera tor -d(2)/dx(2) + q(x, y).