2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/135221In this paper we study the behaviour in time of the trace (the partition function) of the heat semigroup associated with symmetric stable processes in domains of $\Rd$. In particular, we show that for domains with the so called {\it{$R$-smoothness}} property the second terms in the asymptotic as $t\to 0$ involves the surface area of the domain, just as in the case of Brownian motion.Spectral TheoryProbabilitytext