ヨシダ　ミノル   Yoshida Minoru   吉田　稔    所属   神奈川大学  工学部 情報システム創成学科     神奈川大学大学院  工学研究科 工学専攻（情報システム創成領域）    職種   教授 言語種別 英語 発行・発表の年月 2021/08 形態種別 学術雑誌 査読 査読あり 標題 Non-local Markovian symmetric forms on infinite dimensional spaces (1: closability and the quasi regularlity) 執筆形態 共著 掲載誌名 Communications in Mathematical Phyisics 掲載区分 国外 出版社・発行元 Springer-Verlag 巻・号・頁 388,pp.659-706 著者・共著者 Sergio Albeverio et. al. 概要 General theorems on the closability and quasi-regularity of non-local Markovian symmetric forms on probability spaces $(S, {\cal B}(S), \mu)$, with $S$ Fr{\'e}chet spaces such that $S \subset {\mathbb R}^{\mathbb N}$, ${\cal B}(S)$ is the Borel $\sigma$-field of $S$, and $\mu$ is a Borel probability measure on $S$, are introduced.Firstly, a family of non-local Markovian symmetric forms ${\cal E}_{(\alpha)}$, $0 < \alpha < 2$, acting in each given $L^2(S; \mu)$ is defined, the index $\alpha$ characterizing the order of the non-locality.Then, it is shown that all the forms ${\cal E}_{(\alpha)}$ defined on $\bigcup_{n \in {\mathbb N}}C^{\infty}_0({\mathbb R}^n)$ are closable in $L^2(S;\mu)$. Moreover, sufficient conditions under which the closure of the closable forms, that are Dirichlet forms, become strictly quasi-regular, are given. Finally, an existence theorem for Hunt processes properly associated to the Dirichlet forms is given.