A Criterion for Property C

Let Lj be formal partial differential operators in Rn, n ≥ 2, with constant coefficients, N(Lj) = {u: Lju = 0}. We say that the pair {L1, L2} has property C, if and only if, for any compact domain D ⊂ Rn, the set {u1u2} ∀uj ∈ N(Lj) is complete in L2(D). A necessary and sufficient condition for the pair {L1L2} to have property C is given.