摘要
设N为非负整数集,Z是整数集,针对N上不同类型的非负函数h,讨论平方可积Bernoulli泛函空间L^(2)(Z)中广义随机梯度h和平方可积Bernoulli过程空间L 2(Z×N)中广义Skorohod积分δ_(h)的共轭关系.若h是N上非负函数,则▽_(h)与δ_(h)互为共轭算子;若h是N上非负平方可和函数,则▽_(h)和Γ-QBN{■σ,■*σ:σ∈Γ}及其混合积的复合与δ_(h)和相应的共轭Γ-QBN及其混合积的复合相互共轭;不同型的Γ-QBN及其混合积“夹逼”δ_(h)º▽_(h),复合算子可“跳出夹逼”,出现相应QBN及其混合积复合的线性函数.
Let N be a nonnegative integer set,Z be a integer set.For the different types of nonnegative functions h on N,the conjugate relations of generalized random gradient▽_(h)in square integrable Bernoulli functional space L^(2)(Z)and generalized Skorohod integralδ_(h)in square integrable Bernoulli process space L^(2)(Z×N)are discussed.If h is a nonnegative function on N,then▽_(h)andδ_(h)are mutually conjugate operators;If h is a nonnegative square summable function on N,the recombination of▽_(h)andδ_(h)withΓ-QBN and its mixed product are conjugated;For the different types ofΓ-QBN and its mixed product pinchδ_(h)º▽_(h),the composition operators can jump out of the pinch,and the linear function ofΓ-QBN and its mixed product composition are appeared.
作者
周玉兰
魏万瑛
柳翠翠
杨青青
ZHOU Yu-lan;WEI Wan-ying;LIU Cui-cui;YANG Qing-qing(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,China)
出处
《西北师范大学学报（自然科学版）》
CAS
北大核心
2023年第6期30-37,共8页
Journal of Northwest Normal University(Natural Science)
基金
国家自然科学基金资助项目(12261080)。
