Froissart, M.; Asymptotic Behavior and Subtractions in the Mandelstam Representation
Phys. Rev. 123 (1961) 1053;
It is proved that a two-body reaction amplitude involving scalar particles and satisfying Mandelstam's representation is bounded by expressions of the form Csln2s at the forward and backward angles, and C3/4 ln 3/2s 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 ln2s. These restrictions limit the freedom of choice of the subtraction
terms to six arbitrary single spectral functions and one subtraction constant.
Related references See also L. Schwartz, Theorie des distributions, Hermann and Cie, Paris (1951);
S. Mandelstam, Phys. Rev. 112 (1958) 1344;
Froissart upper bound on the total cross sections of hadronic collisions.