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连续时间Guichardet-Fock空间中的Dirichlet形式

Dirichlet Forms in Continuous-Time Guichardet-Fock Space
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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).
作者 李晓慧 周玉兰 房彦兵 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)
出处 《吉林大学学报(理学版)》 CAS 北大核心 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).
关键词 Dirichlet形式 加权计数算子 点态修正随机梯度 Dirichletform weightednumberoperator point-statemodifiedstochasticgradient
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