{"paper":{"title":"Small time asymptotics of spectral heat contents for subordinate killed Brownian motions related to isotropic {\\alpha}-stable processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hyunchul Park, Renming Song","submitted_at":"2018-04-10T16:49:37Z","abstract_excerpt":"In this paper we study the small time asymptotic behavior of the spectral heat content $\\widetilde{Q}_D^{(\\alpha)}(t)$ of an arbitrary bounded $C^{1,1}$ domain $D$ with respect to the \\textit{subordinate killed Brownian motion} in $D$ via an $(\\alpha/2)$-stable subordinator. For all $\\alpha\\in (0,2)$, we establish a two-term small time expansion for $\\widetilde{Q}_D^{(\\alpha)}(t)$ in all dimensions. When $\\alpha\\in (1,2)$ and $d\\geq 2$, we establish a three-term small time expansion for $\\widetilde{Q}_D^{(\\alpha)}(t)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03622","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}