Analytic properties of multiparticle production amplitudes

The local analytic properties of $2\rightarrow 3$ and $2\rightarrow 4$ amplitudes are studied. It is shown that in the neighborhood of any physical point on the mass shell the amplitudes are analytic with respect to the total and partial energies for fixed momentum transfers. The 14 (for $2\rightarrow 3$) and 242 (for $2\rightarrow 4$) different boundary values are expressed in terms of the amplitudes of real processes.