标题： 流形上某些奇异相互作用的哈密顿量的存在性 显示英文标题

标题： Existence of Hamiltonians for Some Singular Interactions on Manifolds

摘要： 在二维和三维黎曼流形中，归一化点相互作用的哈密顿量的存在性以及该模型在二维情况下的相对论扩展的存在性已被证明。 尽管更加困难，仍然可以给出非相对论Lee模型归一化预解式的哈密顿量存在性的证明。 为了直接从预解公式得出这些结果，我们采用了一些来自半群理论的基本工具。 显示英文摘要

摘要： The existence of the Hamiltonians of the renormalized point interactions in two and three dimensional Riemannian manifolds and that of a relativistic extension of this model in two dimensions are proven. Although it is much more difficult, the proof of existence of the Hamiltonian for the renormalized resolvent for the non-relativistic Lee model can still be given. To accomplish these results directly from the resolvent formula, we employ some basic tools from the semigroup theory.