2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73601We describe some connections, via composition, between two functional spaces: the space of (sub)critical branching mechanisms and the space of Bernstein functions. The functions ${\bf e}_α: x\to x^α$ where $x\geq0$ and $0<α\leq 1/2$, and in particular the critical parameter $α=1/2$, play a distinguished role.ProbabilityMSC 60E07text