Abstract: | We consider an operator Aε on L2(\({\mathbb{R}^{{d_1}}} \times {T^{{d_2}}}\)) (d1 is positive, while d2 can be zero) given by Aε = ?div A(ε?1x1,x2)?, where A is periodic in the first variable and smooth in a sense in the second. We present approximations for (Aε ? μ)?1 and ?(Aε ? μ)?1 (with appropriate μ) in the operator norm when ε is small. We also provide estimates for the rates of approximation that are sharp with respect to the order. |