We generalize to several variables Kurbanov and Maksimov’s result that all linear polynomial operators can be expressed as a formal sum ∑∞ k=0 ak(X) D k in terms of the derivative D (or any degree reducing operator) and multiplication by x. In contrast, we characterize those linear operators that can be expressed as ∑∞ k=0 fk(D) X k and give several… (More)