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

Date: 14. 11. 2017

Source: Algebra and functional analysis seminar

Source: 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.

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.