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A periodic differential operator of the form Aε = (Dp)∗g(x/ε)Dp is considered on L2(R); here g(x) is a positive definite symmetric tensor of order 2p periodic with respect to a lattice Γ. The behavior of the resolvent of the operator Aε as ε → 0 is studied. It is shown that the resolvent (Aε + I)−1 converges in the operator norm to the resolvent of the effective operator A0 with constant coefficients. For the norm of the difference of resolvents, an estimate of order ε is obtained. §

Homogenization of periodic differential operators of high order