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In this paper we study the asymptotic behavior, as $t\downarrow 0$, of thespectral heat content $Q^{(\alpha)}_{D}(t)$ for isotropic $\alpha$-stableprocesses, $\alpha\in [1,2)$, in bounded $C^{1,1}$ open sets $D\subset \R^{d}$,$d\geq 2$. Together with the results from \cite{Val2017} for $d=1$ and\cite{GPS19} for $\alpha\in (0,1)$, the main theorem of this paper establishesthe asymptotic behavior of the spectral heat content up to the second term forall $\alpha\in (0,2)$ and $d\geq1$, and resolves the conjecture raised in\cite{Val2017}.

Spectral heat content for {\alpha}-stable processes in C1,1 open sets