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Higher Order Terms of the Spectral Heat Content for Killed Subordinate and Subordinate Killed Brownian Motions Related to Symmetric α-Stable Processes in \({\mathbb {R}}\)

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Abstract

We investigate the 3rd term of the spectral heat content for killed subordinate and subordinate killed Brownian motions on a bounded open interval D = (a,b) in a real line when the underlying subordinators are stable subordinators with index α ∈ (1, 2) or α = 1. We prove that in the 3rd term of the spectral heat content, one can observe the length ba of the interval D.

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Acknowledgements

The author thanks the anonymous referee for carefully reading the manuscript and providing useful suggestions and recommendations.

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Correspondence to Hyunchul Park.

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Park, H. Higher Order Terms of the Spectral Heat Content for Killed Subordinate and Subordinate Killed Brownian Motions Related to Symmetric α-Stable Processes in \({\mathbb {R}}\). Potential Anal 57, 283–303 (2022). https://doi.org/10.1007/s11118-021-09916-1

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  • DOI: https://doi.org/10.1007/s11118-021-09916-1

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