On the real algebra of Denjoy-Carleman classes (Q2474167)

The main result of the paper under review shows that if \(f\) is a nonnegative germ at the origin in the Denjoy--Carleman class \(C_M({\mathbb R}^2,0)\), then \(f\) is the sum of at most two squares in \(C_{M^k}({\mathbb R}^2,0)\), where \(M^k=\{M_{kp}\}_{p\geq0}\). If, in addition to this, \(f^{-1}(0)=0\), then \(f\) is a sum of at most two squares in \(C_M({\mathbb R}^2,0)\).