Representations for Three-Body T-Matrix on Unphysical Sheets: Proofs

A proof is given for the explicit representations which have been formulated in the author's previous work (nucl-th/9505028) for the Faddeev components of three-body T-matrix continued analytically on unphysical sheets of the energy Riemann surface. Also, the analogous representations for analytical continuation of the three-body scattering matrices and resolvent are proved. An algorithm to search for the three-body resonances on the base of the Faddeev differential equations is discussed.