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Those homogeneous polynomials P are characterized for which for arbitrary lower order polynomials Q the partial differential operator (P+Q)(D) admits a continuous linear right inverse if regarded as an operator from the space of all C∞functions on R into itself. It is shown that P has this property if and only if P is of principal type and real up to a complex constant and has no elliptic factor.

Characterization of the homogeneous polynomials P for which (P + Q)(D) admits a continuous linear right inverse for all lower order perturbations Q