E-mail: raedhat@yahoo.com
Abstract. The present paper is devoted to further development of commutative nonstationary field themes; the first studies in this area were performed by K.~Kirchev and V.~Zolotarev \cite{4, 5}. In this paper a more complicated variant of commutative field with nonstationary rank 2, carrying into more general situation for correlation function is studied. A condition of consistency (see (7) below) for commutative field is placed in the basis of the method proposed in \cite{4, 5} and developed in this paper. The following semigroup structures of correlation theory for disturbances and semigroups are used in this case: $T_t (\varepsilon)=\exp (it A_{\varepsilon})$, $A_\varepsilon = A_1 +\varepsilon A_2$, $|\varepsilon| \ll 1$.
AMSclassification. Primary 47D03; Secondary 47C10, 47F05.
Keywords. Commutative nonstationary stochastic fields, correlation function, infinitesimal correlation function, contractive semigroup.