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In this paper, I prove that the sub-Coulomb $A(d,p)B$ reaction amplitude,which is a solution of the three-body Faddeev equations in theAlt-Grassberger-Sandhas (AGS) form, is peripheral if a peripheral is thecorresponding DWBA amplitude. Hence the Faddeev's reaction amplitude for thesub-Coulomb $A(d,p)B$ reactions can also be parametrized in terms of the ANC ofthe $(n\,A)$ bound state. First, I consider the original AGS equations withseparable potentials and prove that such equations are peripheral atsub-Coulomb energies. After that, the two-particle AGS equations are derivedfor the general potentials for sub-Coulomb transfer reactions. The effectiveAGS potentials are expressed in terms of the DWBA amplitudes for thesub-Coulomb reactions. Again, I demonstrate that the amplitude of the $A(d,p)B$transfer reaction obtained from the AGS equation is peripheral and can beparametrized in terms of the ANC for the $(nA)$ bound state because thecorresponding DWBA amplitude is peripheral. Finally, the AGS equations aregeneralized by including the optical nuclear potentials in the same manner asit is done in the DWBA. The obtained two-particle AGS equations contain theDWBA effective potentials with distorted waves generated by the sum of thenuclear optical and the channel Coulomb potentials. The AGS equation for the$A(d,p)B$ reactions is analyzed above the Coulomb barrier and it is shown againthat the reaction amplitude satisfying generalized AGS equation with opticalpotentials depends on the ANC if a peripheral is the DWBA amplitude. Thetwo-body AGS equations are generalized by including the intermediate three-bodycontinuum and more than one bound state in each channel.

Three-body Faddeev equations in two-particle Alt-Grassberger-Sandhas form with Distorted-Wave-Born-approximation amplitudes as effective potentials