Abstract
In the space \(\mathbb{R}^{d}\) , \(d\geq 2\) , we consider divergence form matrix differential operators \(L_{\varepsilon}\) of elliptic type and arbitrary even order \(2m\geq 4\) with measurable \(\varepsilon\) -periodic coefficients, where \(\varepsilon\) is a small parameter. We construct resolvent approximations for these operators with an error of the order of \(\varepsilon^{2}\) in the energy operator \((L^{2}\to H^{m})\) -norm.
