SOMMES DE CARRES DE FONCTIONS DERIVABLES

摘要

We prove that any nonnegative function of class C2m defined in an interval is the sum of two squares of functions of class C". In dimension 2, any nonnegative function f of class C4 is a finite sum of squares of functions of class C2, provided that V4f vanishes at points x satisfying f(x) = ▽2f(x-) = 0.