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Ultrahyperfunctions (UHF)are the generalization and extension to the complex planeof Schwartz´ tempered distributions. This effort is an {f application} to Einstein´s gravity (EG) of themathematical theory of convolution of Ultrahyperfunctions developed by Bollini et al cite{tp3,tp18,tp19,tp20}.A simplified version of these results was given in cite{pr} and, based on them, a Quantum Field Theory (QFT) of EG cite{pr1} was obtained. Any kind of infinities are avoided by recourse to UHF.We will quantize EG by appeal to the {sf most general quantization approach}, the Schwinger-Feynman variational principle, which is more appropriate and rigorous that the popular functional integral method (FIM). FIM is not applicable here because our Lagrangian contains derivative couplings. d We follow works by Suraj N. Gupta and Richard P. Feynman so as toundertake the construction of a EG-QFT. We explicitly use the Einstein Lagrangian as elaboratedby Gupta cite{g1}, but choose a new constraint for the ensuing theory. In this way, we avoid the problem of lack of unitarity for the $S$ matrix that afflicts the procedures ofGupta and Feynman.Simultaneously, we significantly simplify the handling of constraints, which eliminates the need to appeal to ghosts for guarantying unitarityof the theory.Our approach is obviously non-renormalizable. However, this inconvenience can be overcome by appealing tho the mathematical theorydeveloped by Bollini et al. cite{tp3,tp18,tp19,tp20,pr}Such developments were founded in the works of Alexander Grothendieck cite{gro}and in the theory of Ultradistributions of Jose Sebastiao e Silva cite{tp6}(also known as Ultrahyperfunctions).Based on these works, an edifice has been constructed along two decades that is able to quantize non-renormalizable Field Theories (FT).Here we specialize this mathematical theory to discuss EG-QFT. Because we are using a Gupta-Feynman inspired EG Lagrangian, we areable to evade the intricacies of Yang-Mills theories