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If we take into account only the first term of the right- hand part of Fig. 3 we obtain the simplest Hubbard I approximation with consideration only of the chain-type diagrams. 

The diagram Fig. 3 b) is the simplest contribution to correlation function which takes into account the elec- tronic correlations. The diagrams Fig. 3 b), c) and d) are localized and their Fourier representations in real space are independent of momentum. There are also other dia- grams of this kind with irreducible functions G (0) ir 5 , G (0) ir 6 and so on. The coefficients before these diagrams are de- termined by the number 1 2 n n $_{!}$, where 2 n is the perturba- tion theory order of diagram. The last diagram of Fig. 3 is not local and its Fourier representation depends of the momentum. To dynamical mean field theory only the first group of local diagrams of Fig. 3 correspond. 

The transition of the diagram contribution from su- perconducting version to the normal one is realized by 

the condition of equality to zero of the sums of all α − indices of every dynamical quantity. For example such transition of the diagram Fig. 3 b) is conditioned by the equalities α$_{1}$ − α$_{2}$ = 0 and α − α$_{1}$ + α$_{2}$ − α ′ = 0 with solution α$_{1}$ = α$_{2}$ and α = α $^{′}$. 

The summation by α$_{1}$ gives us two equal contributions and the coefficient before diagram increases twofold and becomes 1 instead originally 1 $_{2}$. 

In normal state the correlation function Λ( x | x $^{′}$) has a form depicted on the Fig. 4. 

The new coefficient before the diagrams take into ac- count the existence of different possibilities of transition from superconducting to normal state. 

After discussion of the propagators properties we shall proceed to the main part of our paper and investigate the properties of evolution operator average. 

