连续时间Guichardet-Fock空间中的Dirichlet形式  

Dirichlet Forms in Continuous-Time Guichardet-Fock Space

作　　者：李晓慧[1] 周玉兰 房彦兵[1] 张银 LI Xiaohui;ZHOU Yulan;FANG Yanbing;ZHANG Yin(School of Advanced Interdisciplinary Studies,Ningxia University,Zhongwei 755099,Ningxia Hui Autonomous Region,China;College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China;School of Intelligence Technology,Geely University of China,Chengdu 641402,China)

机构地区：[1]宁夏大学前沿交叉学院,宁夏中卫755099 [2]西北师范大学数学与统计学院,兰州730070 [3]吉利学院智能科技学院,成都641402

出　　处：《吉林大学学报（理学版）》2023年第3期509-516,共8页Journal of Jilin University:Science Edition

基　　金：宁夏自然科学基金(批准号:2020AAC03070);宁夏大学社会科学基金(批准号:sk21015).

摘　　要：首先,用有界算子的重积分研究连续时间Guichardet-Fock空间L^(2)(Γ;η)中的Dirichlet形式(ε,Domε),得到了(ε,Domε)与加权计数算子S_(ω)之间的关系:1)ε(f,g)=〈〈f,S_(ω)g〉〉,f∈Domε,g∈Dom S_(ω);2)ε(f,f)=‖S_(ω)f‖2,Domε=Dom S_(ω),f∈Domε.其次,考虑一类算子半群(C_(0)-半群)(T t)t≥0=(e-tS_(ω))t≥0,证明(ε,Domε)与算子半群之间的关系:ε(f,f)=lim t→0+W_(f):1 t(I-e-tS_(ω)),f∈Domε,其中W_(f):(x)=〈〈xf,f〉〉,x∈L^(2)(Γ;η),I为L^(2)(Γ;η)中的平凡表示.Firstly,we study the Dirichlet forms(ε,Domε)in continuous-time Guichardet-Fock space L^(2)(Γ;η)by means of multiple integral of bounded operator,and obtain the relationε(f,g)=〈〈f,S_(ω)g〉〉,f∈Domε,g∈Dom S_(ω)andε(f,f)=‖S_(ω)f‖2,Domε=Dom S_(ω),f∈Domεbetween(ε,Domε)and the weighted number operator S_(ω).Secondly,we consider a class of operator semigroups(C_(0)-semigroup)(T t)t≥0=(e-tS_(ω))t≥0,and prove the relationε(f,f)=lim t→0+W_(f):1 t(I-e-tS_(ω)),f∈Domεbetween(ε,Domε)and operator semigroup,where W_(f):(x)=〈〈xf,f〉〉,x∈L^(2)(Γ;η),I is the trivial representation in L^(2)(Γ;η).

关 键 词：Dirichlet形式 加权计数算子 点态修正随机梯度 

分 类 号：O211[理学—概率论与数理统计]