Nonlocal quantum field theory within the frameworks of the Bogolyubov axiomatic approach

The construction of both local and two types of nonlocal quantum field theory in the Bogolyubov modified axiomatic approach is continued in exact terms of functional analysis. Infinite variational differentiability by Freslie of the current functional in the surrounding of the K=0 point is proved. Aslo proved is the reduction formula, which is a matrix emelent of any process with elementary particles as vacuum holding from j-polynomial (i.e. polynomial on j-functional and its variational derivatives) in the K=0 point