Constraints on the behaviour of the e+e− hadron annihilation cross section in asymptotically free theories and in theories with anomalous dimensions

A new approach is proposed to the problem of the relationship between the e⁺e^? hadron annihilation cross section and the behaviour of the hadronic vacuum polarization tensor Π_μν(q) in the space-like region. By using this approach based on the principles of functional analysis, one can uniquely transform the information about the behaviour of Π_μν(q) at q² → ?∞, which is available in asymptotically free theories and in theories with anomalous dimensions, into constraints on the e⁺e^? total cross section.