A necessary condition for the local solvability of the operator Pm2(x, D) + P2m − 1(x, D)

AbstractIt is shown that a necessary condition for the local solvability of the operator P(x, D) = Pm2(x, D) + P2m − 1(x, D), where Pm(x, D) is an mth-order homogeneous differential operator of principal type with real coefficients, is that along any null-bicharacteristic strip of Pm(x, ξ) the imaginary part of the sub-principal symbol cannot have an odd-order zero where its real part does not vanish