Expansions with respect to squares, symplectic and poisson structures associated with the Sturm–Liouville problem. I

In the generic position case properties of the variations of scattering data are studied for a smooth fast decreasing potential of the Sturm–Liouville problem. Orthogonality and completeness relations for bilinear combinations of the lost solutions of this problem are formulated in a more precise form and properties of the recursion operator and its resolvent are thoroughly analysed.