论文标题
在无穷小发电机和阿氏扩散的Feynman-kac积分上
On Infinitesimal Generators and Feynman-Kac Integrals of Adelic Diffusion
论文作者
论文摘要
对于每个Prime $ P $，具有正指数的Vladimirov操作员指定$ p $ -ADIC扩散方程式和Skorokhod空间的量度。固定指数的这些措施中的产品（$ p $）是$ p $ - 亚洲路径空间的乘积的概率度量。当且仅当扩散常数的总和$σ$是有限时，Adelic路径才具有完整的度量。 $σ$的有限性意味着有一个Adelic Vladimirov操作员，$δ_ {\ Mathbb a} $，以及一个关联的扩散方程，其基本解决方案促进了Adelic Skorokhod空间上$ p $引起的度量。对于广泛的电势，与AdelicSchrödinger运算符相关的动力学半群具有免费部分$δ_ {\ Mathbb a} $具有路径积分表示。
For each prime $p$, a Vladimirov operator with a positive exponent specifies a $p$-adic diffusion equation and a measure on the Skorokhod space of $p$-adic paths. The product, $P$, of these measures with fixed exponent is a probability measure on the product of the $p$-adic path spaces. The adelic paths have full measure if and only if the sum, $σ$, of the diffusion constants is finite. Finiteness of $σ$ implies that there is an adelic Vladimirov operator, $Δ_{\mathbb A}$, and an associated diffusion equation whose fundamental solution gives rise to the measure induced by $P$ on an adelic Skorokhod space. For a wide class of potentials, the dynamical semigroups associated to adelic Schrödinger operators with free part $Δ_{\mathbb A}$ have path integral representations.
