In this paper we study the asymptotic behavior, as , of the spectral heat content for isotropic α-stable processes, , in bounded open sets , . Together with the results from  for and  for , the main theorem of this paper establishes the asymptotic behavior of the spectral heat content up to the second term for all and , and resolves the conjecture raised in .
Hyunchul Park was supported in part by Research and Creative Project Award from SUNY New Paltz. Renming Song was supported in part by a grant from the Simons Foundation (#429343, Renming Song)
We thank the referee for helpful comments and suggestions. The first-named author is grateful to Professor Kyeong Hun Kim (Korea University, South Korea) for his encouragement while this project was in progress. Part of the research for this project was done while the second-named author was visiting Jiangsu Normal University, where he was partially supported from the National Natural Science Foundation of China (11931004) and by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
"Spectral heat content for α-stable processes in open sets." Electron. J. Probab. 27 1 - 19, 2022. https://doi.org/10.1214/22-EJP752