This paper is a contribution to semiclassical analysis for abstract Schrödinger type operators on locally compact spaces: LetX be a metrizable seperable locally compact space, let μ be a Radon measure on X with a full support. Let (t, x, y) 7→ p(t, x, y) be a strictly positive pointwise consistent μ-heat kernel, and assume that the generator Hp ≥ 0 of the corresponding self-adjoint contraction semigroup in L(X,μ) induces a regular Dirichlet form. Then, given a function Ψ : (0, 1) → (0,∞) such that the limit limt→0+ p(t, x, x)Ψ(t) exists for all x ∈ X , we prove that for every potential w : X → R one has lim t→0+ Ψ(t)tr ( ep )

中文翻译：

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关于 Dirichlet 空间的半经典极限几何

这篇论文是对局部紧空间上抽象薛定谔类型算子的半经典分析的贡献：让X是一个可度量的可分局部紧空间，让μ是一个完全支持的X上的Radon测度。令 (t, x, y) 7→ p(t, x, y) 为严格正的逐点一致 μ-heat 核，并假设 L(X, μ) 诱导出规则的狄利克雷形式。然后，给定一个函数 Ψ : (0, 1) → (0,∞) 使得极限 limt→0+ p(t, x, x)Ψ(t) 对所有 x ∈ X 都存在，我们证明对于每个势 w : X → R one 有 lim t→0+ Ψ(t)tr ( ep )