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

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