Abstract: The well-known example of an equation with real coefficients without solution was given by F.Trèves in 1962. i.e. the operator of the 4^th order ZZZZ is 《without solution》. In this paper we first have discussed some properties of the multidimensional operator of the 4^th order △_k²+n²T²(=Σ_i,k=1ⁿ Z_jZ_jZ_kZ_k).