On Operator Estimates of the Homogenization of Higher-Order Elliptic Systems

In the space $\mathbb R^d$, we consider matrix elliptic operators $L_\varepsilon$ of arbitrary even order $2m\ge 4$ with measurable $\varepsilon$-periodic coefficients, where $\varepsilon$ is a small parameter. We construct an approximation to the resolvent of this operator with an error of the order of $\varepsilon^2$ in the operator $(L^2\to L^2)$-norm.