Approximations of the resolvent for a non-self-adjoint diffusion operator with rapidly oscillating coefficients

A strongly inhomogeneous diffusion operatorwith drift depending on a small parameter ɛ is studied in the space L 2(ℝ n ). The strong inhomogeneity consists in that the coefficients of the operator are ɛ-periodic and, in addition, the drift vector is of the order of ɛ −1. As ɛ → 0, approximations in the operator L 2-norm of order ɛ and ɛ 2 are constructed for the resolvent of the operator. For each of these orders of approximation, an averaged diffusion operator is obtained. A spectral method based on the Bloch representation for an operator with periodic coefficients is used.