Solutions to a system of equations for Cm functions

• Charles Fefferman ^[1] ; Garving K. Luli ^[2]
  1. [1] Princeton University

     Princeton University

     Estados Unidos

     
  2. [2] University of California at Davis
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 37, Nº 3, 2021, págs. 911-963
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.