Meromorphization of Large N QFT

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.