共查询到18条相似文献,搜索用时 109 毫秒
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主要研究基于l2(N)上交互作用Fock空间l2(Γ,{λn})中的梯度算子和散度算子.首先定义交互作用Fock空间l2(Γ,{λn})上的梯度算子和散度算子;然后研究梯度、散度算子所具有的算子性质;最后研究由梯度算子和散度算子构成的复合算子与该空间中其他算子的关系.结果表明:交互作用Fock空间l2(Γ,{λn})中... 相似文献
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吴焕春 《数学的实践与认识》2008,38(23)
Fock空间是由整函数组成的具有再生核的Hilbert空间.Fock空间上的乘法算子的定义域不是整个Fock空间,它在Fock空间上是稠定的.研究了Fock空间上的乘法算子的性质,对其值域进行了刻画,并得出了乘法算子作用在Fock空间的拟不变子空间上值域余一维的充要条件. 相似文献
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本文表明$\mathbb{C}^N$上的Fock空间上有界可逆加权复合算子是酉算子的非零常数倍,这是关于$\mathbb{C}^N$上的Fock空间上可逆加权复合算子已有刻画的一个补充,也是对$\mathbb{C}$上的Fock空间上相应结果的推广. 相似文献
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本文首先定义了内积函数,这个概念推广了内积的定义.然后定义了Hilbert空间(H,〈·,·〉)上由严格正算子A诱导的范数,这个范数与由〈·,·〉诱导的范数是等价的.进一步,证明了所有的内积函数与线性有界的严格正算子全体之间存在一一对应关系. 相似文献
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通过符号映射研究Fock空间之正交补空间上对偶Toeplitz代数的结构,得到了Fock空间上对偶Toeplitz代数的一个短正合序列.并研究了对偶Toeplitz算子谱的性质. 相似文献
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混沌表示是白噪声分析的关键.考虑目前的基于广义Fock空间的两种混沌分解所依赖的n粒子空间的内积,本文得到了这两种n粒子空间的内积以及两种广义Fock空间的关系. 相似文献
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本文给出了CN上Fock空间上有限余维加权复合算子的完全刻画,该刻画与Fock空间上循环向量的刻画密切相关.主要结论表明,Fock空间上一个有界加权复合算子是有限余维的当且仅当其复合符号是1次可逆解析多项式,且当N=1时,其加权符号至多有有限个零点;当N≥2时,其加权符号没有零点. 相似文献
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《Mathematical Methods in the Applied Sciences》2018,41(13):5308-5326
The aim of this paper is to study complete polynomial systems in the kernel space of conformally invariant differential operators in higher spin theory. We investigate the kernel space of a generalized Maxwell operator in 3‐dimensional space. With the already known decomposition of its homogeneous kernel space into 2 subspaces, we investigate first projections from the homogeneous kernel space to each subspace. Then, we provide complete polynomial systems depending on the given inner product for each subspace in the decomposition. More specifically, the complete polynomial system for the homogenous kernel space is an orthogonal system wrt a given Fischer inner product. In the case of the standard inner product in L2 on the unit ball, the provided complete polynomial system for the homogeneous kernel space is a partially orthogonal system. Further, if the degree of homogeneity for the respective subspaces in the decomposed kernel spaces approaches infinity, then the angle between the 2 subspaces approaches π/2. 相似文献
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This paper studies a class of weighted composition operators and their spectrum on the Fock space.As an application,bounded self-adjoint,a class of complex symmetric weighted composition operators on the Fock space are characterized. 相似文献
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Xiang Fang 《Journal of Functional Analysis》2007,253(1):359-372
In recent years various advances have been made with respect to the Nevanlinna-Pick kernels, especially on the symmetric Fock space, while the development on the Hardy space over the polydisc is relatively slow. In this paper, several results known on the symmetric Fock space are proved for the Hardy space over the polydisc. The known proofs on the symmetric Fock space make essential use of the Nevanlinna-Pick properties.Specifically, we study several integer-valued numerical invariants which are defined on an arbitrary invariant subspace of the vector-valued Hardy spaces over the polydisc. These invariants include the Samuel multiplicity, curvature, fiber dimension, and a few others.A tool used to overcome the difficulty associated with non-Nevanlinna-Pick kernels is Tauberian theory. 相似文献
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本文研究了不定度规空间空间中的无穷维Hamilton算子.利用Plus算子存在极大不变子空间的性质,获得了无穷维Hamilton算子在Krein空间中存在极大确定不变子空间的充分条件. 相似文献
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本文讨论了Fock空间上以径向函数和拟齐次函数为符号的Toeplitz算子的代数性质,给出了两个以径向函数为符号的Toeplitz算子的积仍为Toeplitz算子的充分必要条件,并且研究了以拟齐次函数为符号的Toeplitz算子的交换性. 相似文献
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Kamal Diki 《Mathematical Methods in the Applied Sciences》2019,42(6):2124-2141
Inspired from the Cholewinski approach, we investigate a family of Fock spaces in the quaternionic slice hyperholomorphic setting as well as some associated quaternionic linear operators. In a particular case, we reobtain the slice hyperholomorphic Fock space on quaternions. 相似文献