Fundamental Properties of Perturbation-Theoretical Integral Representations

The integral representations proposed previously are extended to the case of general transition amplitudes. The analyticity domain of any term in these representations is found explicitly. It is proved that any function analytic in this domain has an integral representation of the above type and then the weight function in this representation is uniquely determined. It is also proved in the case of two-particle scattering that the amplitude uniquely determines the three weight functions in its integral representation if they satisfy certain conditions.