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2022 Spectral heat content for α-stable processes in C1,1 open sets
Hyunchul Park, Renming Song
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Electron. J. Probab. 27: 1-19 (2022). DOI: 10.1214/22-EJP752


In this paper we study the asymptotic behavior, as t0, of the spectral heat content QD(α)(t) for isotropic α-stable processes, α[1,2), in bounded C1,1 open sets DRd, d2. 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 d1, and resolves the conjecture raised in [2].

Funding Statement

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.


Download Citation

Hyunchul Park. Renming Song. "Spectral heat content for α-stable processes in C1,1 open sets." Electron. J. Probab. 27 1 - 19, 2022.


Received: 17 April 2021; Accepted: 1 February 2022; Published: 2022
First available in Project Euclid: 11 February 2022

Digital Object Identifier: 10.1214/22-EJP752

Primary: 60J76

Keywords: asymptotic behavior , spectral heat content , Stable processes


Vol.27 • 2022
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