The parametrix of elliptic operators with infinitely many independent variables

Among the differential equations with infinitely many independent variables most attention has been paid to second-order parabolic equations. The paper begins with a rief review of the results obtained for the Cauchy problem for such equations. The parametrix is constructed for a ertain class of elliptic differential operators with infinitely many variables. This parametrix is generated by a easure in the corresponding function space. A omposition formula for an elliptic differential operator and its parametrix is proved. Applications are given to the theory of the solubility of elliptic equations with infinitely many variables.