Nullstellensatz for systems of PDEs
Amol Sasane (London School of Economics)
Thursday 20th November, 2008 15:00-16:00 203
Given an ideal I in the polynomial ring C[x1,...xn], the variety of I is the set of common zeros in C^n of all the polynomials that belong to I, and the Hilbert Nullstellensatz states that there is a bijective correspondence between these varieties and radical ideals of the polynomial ring. On the other hand, if one has a system of linear constant coefficient partial differential equations, one can consider its zeros, that is, its solutions in various function and distribution spaces. The question then arises as to what is the analogue of the Hilbert Nullstellensatz in this set up. In this talk we give such a result when the underlying solution space is the space of distributions that are tempered in the spatial direction.