Factorization of nonlinear supersymmetry in one-dimensional quantum mechanics II: proofs of theorems on reducibility

In this part we continue the investigation of factorization of supersymmetric transformations in one-dimensional Quantum Mechanics into chains of elementary Darboux transformations with nonsingular coefficients. The definition is given for the potential class invariant against Darboux–Crum transformations and, further on, a number of lemmas and theorems substantiating the conjectures set forth on reducibility of differential operators for spectral equivalence transformations is proven. The analysis in general case is performed with all necessary proofs.