Faddeev’s equations in differential form: Completeness of physical and spurious solutions and spectral properties

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Abstract
Faddeev type equations are considered in differential form as eigenvalue equations for non-self-adjoint channel space (matrix) Hamiltonians HF. For these equations in both the spatially confined and infinite systems, the nature of the spurious (nonphysical) solutions is obvious. Typically, these together with the physical solutions (given extra technical assumptions) generate a regular biorthogonal system for the channel space. This property may be used to provide an explicit functional calculus for the then real eigenvalue scalar spectral HF, to show that ±iHF generate uniformly bounded C0 semigroups and to simply relate HF to self-adjoint Hamiltonian-like operators. These results extend to the four-channel Faddeev type equations where the breakup channel is included explicitly.