Spectral Heat Content for Time-Changed Killed Brownian Motions

The spectral heat content is investigated for time-changed killed Brownian motions on $$C^{1,1}$$ open sets, where the time change given by either a subordinator or an inverse subordinator, with underlying Laplace exponent being regularly varying at $$\infty $$ index $$\beta \in (0,1)$$ . In case of subordinators, asymptotic limit in small shown to involve probabilistic term depending only contrast, this universality holds when (\frac{1}{2}, 1)$$