{"paper":{"title":"Pointwise estimates for the ground states of singular Dirichlet fractional Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Ali Beldi, Ali BenAmor, Nedra Belhajrhouma","submitted_at":"2012-11-02T20:38:15Z","abstract_excerpt":"We establish sharp pointwise estimates for the ground states of some singular fractional Schr\\\"odinger operators on relatively compact Euclidean subsets. The considered operators are of the type $(-\\Delta)^{\\alpha/2}|_\\Om-c|x|^{-\\alpha}$, where $(-\\Delta)^{\\alpha/2}|_\\Om$ is the fraction-Laplacien on an open subset $\\Om$ in $\\R$ with zero exterior condition and $0<c\\leq(\\frac{d-\\alpha}{2})^2$. The intrinsic ultracontractivity property for such operators is discussed as well and a sharp large time asymptotic for their heat kernels is derived."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0560","kind":"arxiv","version":1},"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"}