arXiv subjects

Toshinao Kagawa

Publications and source records attributed to Toshinao Kagawa.

3 recordsLinked to original sources

arXiv2023

A general formulation of Non-Local Dirichlet forms on infinite dimensional topological vector spaces and its applications, and corresponding subjects: Seminar at Univ. Lisboa,2023

A concise explanations on the results given by Non-local Markovian Symmetric Forms on Infinite Dimensional Spaces I, CMP 2021, by Sergio Albeverio, Minoru W. Yoshida, et.al., and Non-local Markovian Symmetric Forms on Infinite Dimensional Spaces Part 2, Potential Analysis 2022, by Sergio Albeverio, Minoru W. Yoshida, et.al.are given as a digestive fashion.

math.FA↗

arXiv2021

Non-local Markovian symmetric forms on infinite dimensional spaces

General theorems on the closability and quasi-regularity of non-local Markovian symmetric forms on probability spaces $(S, {\cal B}(S), μ)$, with $S$ Fr{é}chet spaces such that $S \subset {\mathbb R}^{\mathbb N}$, ${\cal B}(S)$ is the Borel $σ$-field of $S$, and $μ$ is a Borel probability measure on $S$, are introduced. Firstly, a family of non-local Markovian symmetric forms ${\cal E}_{(α)}$, $0 < α< 2$, acting in each given $L^2(S; μ)$ is defined, the index $α$ characterizing the order of the non-locality. Then, it is shown that all the forms ${\cal E}_{(α)}$ defined on $\bigcup_{n \in {\mathbb N}} C^{\infty}_0({\mathbb R}^n)$ are closable in $L^2(S;μ)$. 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. The application of the above theorems to the problem of stochastic quantizations of Euclidean $Φ^4_d$ fields, for $d =2, 3$, by means of these Hunt processes is indicated.

math.PR↗

arXiv2021

Non-local Markovian symmetric forms on infinite dimensional spaces; Part 2. Examples: non local stochastic quantization of space cut-off quantum fields and infinite particle systems

The general framework on the non-local Markovian symmetric forms on weighted $l^p$ $(p \in [1, \infty])$ spaces constructed by [A,Kagawa,Yahagi,Y 2020], by restricting the situation where $p =2$, is applied to such measure spaces as the space cut-off $P(ϕ)_2$ Euclidean quantum field, the $2$-dimensional Euclidean quantum fields with exponential and trigonometric potentials, and the field describing a system of an infinite number of classical particles. For each measure space, the Markov process corresponding to the {\it{non-local}} type stochastic quantization is constructed.

math-ph↗