# Jaka Cimprič: Local linear dependence of linear partial differential operators

Date of publication: 14. 11. 2017

Algebra and functional analysis seminar

Četrtek, 16. 11. 2017, ob 12:30 v predavalnici 2.03, FMF, Jadranska 21, Ljubljana

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.