2019/08/31 by Thilliez, Vincent
#26E10 #30E10 #32W05 #46E25 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.1909.00177
We study the regularity of smooth functions f defined on an open set of ℝn and such that, for certain integers p≥ 2, the powers fp :x↦ (f(x))p belong to a Denjoy-Carleman class CM associated with a suitable weight sequence M. Our main result is a statement analogous to a classic theorem of H. Joris on C^∞ functions: if a function f:ℝ→ℝ is such that both functions fp and fq with gcd(p,q)=1 are of class CM on ℝ, and if the weight sequence M satisfies the so-called moderate growth assumption, then f itself is of class CM. Various ancillary results, corollaries and examples are presented.