Representations for three-body $T$-matrix on unphysical sheets. I

Explicit representations are formulated for the Faddeev components of three-body $T$-matrix continued analytically on unphysical sheets of the energy Riemann surface. According to the representations, the $T$-matrix is obviously expressed in terms of its components taken on the physical sheet only. The representations for $T$-matrix are used to construct similar representations for analytical continuation of three-body scattering matrices and resolvent. Domains on unphysical sheets are described where the representations obtained can be applied.