Spectral heat content for α-stable processes in C^1,1 open sets

In this paper we study the asymptotic behavior, as t↓0, of the spectral heat content QD^(α)(t) for isotropic α-stable processes, α∈[1,2), in bounded C^1,1 open sets D⊂R^d, d≥2. Together with the results from [2] for d=1 and [7] for α∈(0,1), the main theorem of this paper establishes the asymptotic behavior of the spectral heat content up to the second term for all α∈(0,2) and d≥1, and resolves the conjecture raised in [2].