Heat content for stable processes in domains of $\R^d$

Abstract

This paper studies the small time behavior of the heat content of rotationally invariant $\alpha$--stable processes, $0<\alpha \leq 2$, in domains in $\R^d$. Unlike the asymptotics for the heat trace, the behavior of the heat content differs depending on the ranges $0<\alpha<1$, $\alpha=1$ and $1<\alpha\leq 2$.