  We find general relations between RG equations and planar
unitarity-analyticity. These relations are summarized in meromorphization
procedure, generalizing the Pad\'e approximation in the limit of infinite
order. We also investigate confinement conditions for the mass spectrum in
asymptoticaly free QFT and lay down systematic framework for {\alpha} expansion
suggested in previous papers. The new relations for meromorphization of
symmetric conformal tensors are found and studied. Explicit intergal
representation for the triple string vertex {\Gamma} is found. This corresponds
to resonanse theory with infinite number of masses and Lagrangean
\PhiQ\Phi+\Gamma\Phi^3.
