{"paper":{"title":"On the geometry of semiclassical limits on Dirichlet spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR","math.SP"],"primary_cat":"math.DG","authors_text":"Batu G\\\"uneysu","submitted_at":"2017-01-18T10:15:52Z","abstract_excerpt":"This paper is a contribution to semiclassical analysis for abstract Schr\\\"odinger type operators on locally compact spaces: Let $X$ be a metrizable seperable locally compact space, let $\\mu$ be a Radon measure on $X$ with a full support. Let $(t,x,y)\\mapsto p(t,x,y)$ be a strictly positive pointwise consistent $\\mu$-heat kernel, and assume that the generator $H_p\\geq 0$ of the corresponding self-adjoint contraction semigroup in $L^2(X,\\mu)$ induces a regular Dirichlet form. Then, given a function $\\Psi : (0,1)\\to (0,\\infty)$ such that the limit $\\lim_{t\\to 0+}p(t,x,x)\\Psi (t)$ exists for all $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04998","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"}