Small time asymptotics of spectral heat contents for subordinate killed Brownian motions related to isotropic α-stable processes

In this paper, we study the small time asymptotic behavior of the spectral heat content (Formula presented.) of an arbitrary bounded (Formula presented.) domain (Formula presented.) with respect to the subordinate killed Brownian motion in (Formula presented.) via an (Formula presented.) -stable subordinator. For all (Formula presented.), we establish a two-term small time expansion for (Formula presented.) in all dimensions. When (Formula presented.) and (Formula presented.), we establish a three-term small time expansion for (Formula presented.).