The representation of generalized number operator acting on the Bernoulli functionals space(Bernoulli泛函空间中广义计数算子的表示)
得到离散时间正规鞅平方可积泛函空间L2(M)中广义计数算子Nh的5种表示：（1）量子Bernoulli噪声（quantum Bernoulli noises，QBN）的加权表示；（2）Nh的谱表示，广义计数算子Nh以h-计数测度#h的值域为其点谱；（3）Nh的“对角化”表示，Nh可表示为L2(M)的标准正交基{Zσ；σ∈Γ}所生成的一维对角化正交投影算子的加权极限；（4）广义Skorohod积分-广义随机梯度表示，Nh可表示为互共轭算子δh和∇h的复合算子；（5）对N上的任意非负函数h，可构造一列有界广义计数算子，Nh恰为该有界广义计数算子的强极限，当h可和时，Nh为该有界广义计数算子的一致极...
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| Format: | Article |
| Language: | zho |
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Zhejiang University Press
2022-05-01
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| Series: | Zhejiang Daxue xuebao. Lixue ban |
| Subjects: | |
| Online Access: | https://doi.org/10.3785/j.issn.1008-9497.2022.03.008 |
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| author | ZHOUYulan(周玉兰) CHENJia(陈嘉) KONGHuafang(孔华芳) XUERui(薛蕊) CHENGXiuqiang(程秀强) |
| author_facet | ZHOUYulan(周玉兰) CHENJia(陈嘉) KONGHuafang(孔华芳) XUERui(薛蕊) CHENGXiuqiang(程秀强) |
| author_sort | ZHOUYulan(周玉兰) |
| collection | DOAJ |
| description | 得到离散时间正规鞅平方可积泛函空间L2(M)中广义计数算子Nh的5种表示：（1）量子Bernoulli噪声（quantum Bernoulli noises，QBN）的加权表示；（2）Nh的谱表示，广义计数算子Nh以h-计数测度#h的值域为其点谱；（3）Nh的“对角化”表示，Nh可表示为L2(M)的标准正交基{Zσ；σ∈Γ}所生成的一维对角化正交投影算子的加权极限；（4）广义Skorohod积分-广义随机梯度表示，Nh可表示为互共轭算子δh和∇h的复合算子；（5）对N上的任意非负函数h，可构造一列有界广义计数算子，Nh恰为该有界广义计数算子的强极限，当h可和时，Nh为该有界广义计数算子的一致极限。 |
| first_indexed | 2024-04-24T16:52:21Z |
| format | Article |
| id | doaj.art-ab834d2eb06d41df8d9ecb7d762361a0 |
| institution | Directory Open Access Journal |
| issn | 1008-9497 |
| language | zho |
| last_indexed | 2024-04-24T16:52:21Z |
| publishDate | 2022-05-01 |
| publisher | Zhejiang University Press |
| record_format | Article |
| series | Zhejiang Daxue xuebao. Lixue ban |
| spelling | doaj.art-ab834d2eb06d41df8d9ecb7d762361a02024-03-29T01:58:40ZzhoZhejiang University PressZhejiang Daxue xuebao. Lixue ban1008-94972022-05-0149331632310.3785/j.issn.1008-9497.2022.03.008The representation of generalized number operator acting on the Bernoulli functionals space(Bernoulli泛函空间中广义计数算子的表示)ZHOUYulan(周玉兰)0https://orcid.org/0000-0003-4831-7149CHENJia(陈嘉)1KONGHuafang(孔华芳)2XUERui(薛蕊)3CHENGXiuqiang(程秀强)4College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China(西北师范大学 数学与统计学院，甘肃 兰州 730070)College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China(西北师范大学 数学与统计学院，甘肃 兰州 730070)College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China(西北师范大学 数学与统计学院，甘肃 兰州 730070)College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China(西北师范大学 数学与统计学院，甘肃 兰州 730070)College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China(西北师范大学 数学与统计学院，甘肃 兰州 730070)得到离散时间正规鞅平方可积泛函空间L2(M)中广义计数算子Nh的5种表示：（1）量子Bernoulli噪声（quantum Bernoulli noises，QBN）的加权表示；（2）Nh的谱表示，广义计数算子Nh以h-计数测度#h的值域为其点谱；（3）Nh的“对角化”表示，Nh可表示为L2(M)的标准正交基{Zσ；σ∈Γ}所生成的一维对角化正交投影算子的加权极限；（4）广义Skorohod积分-广义随机梯度表示，Nh可表示为互共轭算子δh和∇h的复合算子；（5）对N上的任意非负函数h，可构造一列有界广义计数算子，Nh恰为该有界广义计数算子的强极限，当h可和时，Nh为该有界广义计数算子的一致极限。https://doi.org/10.3785/j.issn.1008-9497.2022.03.008算子谱广义计数算子对角化算子广义skorohod积分广义随机梯度 |
| spellingShingle | ZHOUYulan(周玉兰) CHENJia(陈嘉) KONGHuafang(孔华芳) XUERui(薛蕊) CHENGXiuqiang(程秀强) The representation of generalized number operator acting on the Bernoulli functionals space(Bernoulli泛函空间中广义计数算子的表示) Zhejiang Daxue xuebao. Lixue ban 算子谱 广义计数算子 对角化算子 广义skorohod积分 广义随机梯度 |
| title | The representation of generalized number operator acting on the Bernoulli functionals space(Bernoulli泛函空间中广义计数算子的表示) |
| title_full | The representation of generalized number operator acting on the Bernoulli functionals space(Bernoulli泛函空间中广义计数算子的表示) |
| title_fullStr | The representation of generalized number operator acting on the Bernoulli functionals space(Bernoulli泛函空间中广义计数算子的表示) |
| title_full_unstemmed | The representation of generalized number operator acting on the Bernoulli functionals space(Bernoulli泛函空间中广义计数算子的表示) |
| title_short | The representation of generalized number operator acting on the Bernoulli functionals space(Bernoulli泛函空间中广义计数算子的表示) |
| title_sort | representation of generalized number operator acting on the bernoulli functionals space bernoulli泛函空间中广义计数算子的表示 |
| topic | 算子谱 广义计数算子 对角化算子 广义skorohod积分 广义随机梯度 |
| url | https://doi.org/10.3785/j.issn.1008-9497.2022.03.008 |
| work_keys_str_mv | AT zhouyulanzhōuyùlán therepresentationofgeneralizednumberoperatoractingonthebernoullifunctionalsspacebernoullifànhánkōngjiānzhōngguǎngyìjìshùsuànzidebiǎoshì AT chenjiachénjiā therepresentationofgeneralizednumberoperatoractingonthebernoullifunctionalsspacebernoullifànhánkōngjiānzhōngguǎngyìjìshùsuànzidebiǎoshì AT konghuafangkǒnghuáfāng therepresentationofgeneralizednumberoperatoractingonthebernoullifunctionalsspacebernoullifànhánkōngjiānzhōngguǎngyìjìshùsuànzidebiǎoshì AT xueruixuēruǐ therepresentationofgeneralizednumberoperatoractingonthebernoullifunctionalsspacebernoullifànhánkōngjiānzhōngguǎngyìjìshùsuànzidebiǎoshì AT chengxiuqiangchéngxiùqiáng therepresentationofgeneralizednumberoperatoractingonthebernoullifunctionalsspacebernoullifànhánkōngjiānzhōngguǎngyìjìshùsuànzidebiǎoshì AT zhouyulanzhōuyùlán representationofgeneralizednumberoperatoractingonthebernoullifunctionalsspacebernoullifànhánkōngjiānzhōngguǎngyìjìshùsuànzidebiǎoshì AT chenjiachénjiā representationofgeneralizednumberoperatoractingonthebernoullifunctionalsspacebernoullifànhánkōngjiānzhōngguǎngyìjìshùsuànzidebiǎoshì AT konghuafangkǒnghuáfāng representationofgeneralizednumberoperatoractingonthebernoullifunctionalsspacebernoullifànhánkōngjiānzhōngguǎngyìjìshùsuànzidebiǎoshì AT xueruixuēruǐ representationofgeneralizednumberoperatoractingonthebernoullifunctionalsspacebernoullifànhánkōngjiānzhōngguǎngyìjìshùsuànzidebiǎoshì AT chengxiuqiangchéngxiùqiáng representationofgeneralizednumberoperatoractingonthebernoullifunctionalsspacebernoullifànhánkōngjiānzhōngguǎngyìjìshùsuànzidebiǎoshì |