共查询到20条相似文献,搜索用时 93 毫秒
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四元数Hilbert空间在应用物理科学特别是量子物理中占有重要地位.本文讨论四元数Hilbert空间的框架理论, 在四元数Hilbert空间中引入了Riesz基的概念, 在此基础上刻画了Riesz基,给出了它们的一些等价条件; 特别地, 得到了四元数Hilbert空间中的一个序列是Riesz基的充要条件是它是一个具有双正交序列的完备Bessel序列,且它的双正交序列也是一个完备Bessel序列; 并进一步证明了双正交序列中一个序列的完备性可以从特征刻画中去除.文中举例说明了双正交性、完备性和Bessel性质之间的关系. 相似文献
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关于算术级数的幂次和 总被引:6,自引:0,他引:6
主要研究了ζ函数关于模 q剩余类部分和,不仅得出了一个重要的渐近公式,而且将Kubert恒等式推广到赫尔维茨ζ函数、欧拉双Γ函数和贝努利多项式上. 相似文献
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匡继昌 《数学物理学报(A辑)》2013,33(1):1-5
基于利用一个积分恒等式的新技巧,建立了赋范线性空间中新的Hilbert型积分不等式.这些新的结果包含了n维欧氏空间中n重积分的Hilbert型积分不等式作为其特殊情形. 相似文献
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《中国科学:数学》2016,(4)
本文考虑了Hilbert空间中一些g-框架类展开式以及g-Riesz-Fischer序列.首先讨论了Hilbert空间中一类算子序列,该类算子序列不必是g-Bessel序列.本文证明了在某些条件下g-框架类展开式存在并且这些展开式保持了通常意义下的能量最小性质.然后讨论了满足下g-框架条件的算子序列,这些算子序列不必满足上g-框架界,得到了Hilbert空间的子空间中的g-框架类展开式,并且给出了一个满足下g-框架条件的算子序列的一个刻画.最后讨论了Hilbert空间中的g-Riesz-Fischer序列,该类算子序列与满足下g-框架条件的算子序列紧密相关,得到了g-Riesz-Fischer序列的一些刻画. 相似文献
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本文研究了Hilbert空间中的有效序列,通过引入序列的伴随序列,给出了有效序列的一个等价刻画,接着讨论了保持向量序列有效性的线性算子的性质,证明了一个线性算子将任意有效序列映射为有效序列当且仅当它是酉算子;最后,给出了正规正交基中添加一个单位向量后所得到的序列是有效序列的一个充要条件. 相似文献
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《数学物理学报(A辑)》2017,(2)
该文在Hilbert空间中一般的框架序列扰动形式下,利用正交投影的性质和对偶框架的性质研究了原序列张成的闭子空间与扰动序列张成的闭子空间的关系,并探讨了局部框架的一般扰动对fusion框架系统稳定性的影响.这些结果推广和改进了由Casazza,Kutyniok和Li等得到的著名结果. 相似文献
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p-除环上子空间的交与和 总被引:3,自引:2,他引:1
李桃生 《数学物理学报(A辑)》1995,(4)
本文讨论p-除环上子空间的交与和的关系,用Abel范畴中裂正合序列的性质证明矩阵秩的恒等式和维数公式. 相似文献
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Identities on Bell polynomials and Sheffer sequences 总被引:1,自引:0,他引:1
In this paper, we study exponential partial Bell polynomials and Sheffer sequences. Two new characterizations of Sheffer sequences are presented, which indicate the relations between Sheffer sequences and Riordan arrays. Several general identities involving Bell polynomials and Sheffer sequences are established, which reduce to some elegant identities for associated sequences and cross sequences. 相似文献
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The main theorem proved in this paper consists of a multiplicative distribution formula for the Jacobi forms in two variables associated to Klein forms. This gives stronger versions of distribution formulae appearing in the literature. Indeed, as a first consequence of the main theorem, we deduce an optional proof of the distribution formula true for any elliptic function first found by Kubert and as a second consequence, we prove an ameliorated distribution formula for a certain zeta function previously treated by Coates, Kubert and Robert. Moreover, our main theorem provides the exact root of unity appearing in the distribution formula of Jarvis and Wildeshaus, a fact which could be useful in the K-theory of elliptic curves or more precisely, in the investigation of the elliptic analogue of Zagier's conjecture linking regulators and polylogarithms. 相似文献
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Sheng-liang Yang 《Discrete Mathematics》2008,308(1):51-58
Using the exponential generating function and the Bell polynomials, we obtain several new identities for the binomial sequences. As applications, some interesting identities are established for the Abel polynomials, exponential polynomials and factorial powers. 相似文献
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三对角线阵行列式恒等式及应用 总被引:1,自引:0,他引:1
本文导出了求三对角线阵行列式的显式表示.这个恒等式可应用于研究三对角线阵的逆矩阵和特征值性质以及求某些正交多项式的显式表示,并能由此导出一类有用的恒等式. 相似文献
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We characterize the sequences of orthogonal polynomials on the unit circle whose derivatives are also orthogonal polynomials on the unit circle. Some relations for the sequences of derivatives of orthogonal polynomials are provided. Finally, we pose some problems about orthogonality-preserving maps and differential equations for orthogonal polynomials on the unit circle. 相似文献
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VIDYA VENKATESWARAN 《Transformation Groups》2012,17(1):259-302
It is well known that if one integrates a Schur function indexed by a partition λ over the symplectic (resp. orthogonal) group,
the integral vanishes unless all parts of λ have even multiplicity (resp. all parts of λ are even). In a recent paper of Rains
and Vazirani, Macdonald polynomial generalizations of these identities and several others were developed and proved using
Hecke algebra techniques. However, at q = 0 (the Hall–Littlewood level), these approaches do not work, although one can obtain the results by taking the appropriate
limit. In this paper, we develop a direct approach for dealing with this special case. This technique allows us to prove some
identities that were not amenable to the Hecke algebra approach. Moreover, we are able to generalize some of the identities
by introducing extra parameters. This leads us to a finite-dimensional analog of a recent result of Warnaar, which uses the
Rogers–Szegő polynomials to unify some existing summation type formulas for Hall–Littlewood functions. 相似文献
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我们给出了马欣荣的关于$(f, g)$-反演的三种应用. 在$(f, g)$-演中通过取具体的函数和序列, 我们推出了一些关于超几何级数与调和数的恒等式. 然后我们给出了一些关于$q$-超几何项的反演关系. 最后, 我们将$(f, g)$-反演和$q$-微分算子结合, 得到了一些$q$-级数恒等式. 相似文献
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《Journal of Computational and Applied Mathematics》2001,137(1):109-122
We find necessary and sufficient conditions for some linear combinations of two sequences of orthogonal polynomials to be again orthogonal. 相似文献
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将二项式系数的性质应用到Lucas数列的研究中,并结合Fibonacci数列与Lucas数列的恒等式得到几个有趣的Lucas数列的同余式. 相似文献
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Let , ? be classes of modules, we introduce and characterize orthogonal dimensions of modules and rings by the orthogonal classes of modules ⊥, ⊥ ?, and T . For an almost excellent extension S ≥ R, we give the criteria to test some identities of orthogonal dimensions of modules and rings. As corollaries, some known results are obtained or extended. 相似文献