Resumen de Solutions to a system of equations for Cm functions

Charles L. Fefferman , Garving K. Luli

• Fix m≥0, and let A=(Aij(x))1≤i≤N,1≤j≤M be a matrix of semialgebraic functions on Rn or on a compact subset E⊂Rn. Given f=(f1,…,fN)∈C∞(Rn,RN), we consider the following system of equations:

  ∑j=1MAij(x)Fj(x)=fi(x)for i=1,…,N.

  In this paper, we give algorithms for computing a finite list of linear partial differential operators such that AF=f admits a Cm(Rn,RM) solution F=(F1,…,FM) if and only if f=(f1,…,fN) is annihilated by the linear partial differential operators.