Asymptotic Behavior and Subtractions in the Mandelstam Representation

It is proved that a two-body reaction amplitude involving scalar particles and satisfying Mandelstam's representation is bounded by expressions of the form Csln^2s at the forward and backward angles, and Cs^3{4}ln^3{2}s at any other fixed angle in the physical region, C being a constant, s being the total squared c. m. energy. This corresponds to cross sections increasing at most like ln^2s. These restrictions limit the freedom of choice of the subtraction terms to six arbitrary single spectral functions and one subtraction constant.