Power substitution in quasianalytic Carleman classes

Lev Buhovsky, Avner Kiro, Sasha Sodin

Consider an equation of the form $f(x)=g(x^k)$, where $k>1$ and $f(x)$ is a function in a given Carleman class of smooth functions. For each $k$, we construct a Carleman-type class…