Jaka Cimprič: Local linear dependence of linear partial differential operators

Abstract: I will outline two nullstellensatz type results for linear partial differential operators with polynomial coefficients:
1) Given L_1,...,L_k characterize all L such that L_1 f=...=L_k f=0 implies L f=0 for all analytic f
2) Given L_1,...,L_k characterize all L such that <L_1 f,g>=...=<L_k f,g>=0 implies <L f,g>=0 for all infinitely differentiable f ,g with compact support
The second one can be rephrased in terms of the reflexive closure from the theory of locally linearly dependent operators.
Both manuscripts are available on Arxiv.