Abstract: In, we consider a selfadjoint operator,, of the form (Formula presented.) where. It is assumed that a function is bounded, positive definite, periodic in each variable, and is such that. A rigorous definition of the operator is given in terms of the corresponding quadratic form. It is proved that the resolvent converges in the operator norm on to the operator as. Here, is an effective operator of the same form with the constant coefficient equal to the mean value of. We obtain an error estimate of order for, for, and for. In the case where, the result is refined by taking the correctors into account.