On the one--dimensional spectral Heat content for stable processes

Abstract

This paper provides the second term in the small time asymptotic expansion of the spectral heat content of a rotationally invariant $\alpha$--stable process, $0<\alpha \le 2$, for the interval $(a,b)$. The small time behavior of the spectral heat content turns out to be linked to the distribution of the supremum and infimum processes.