MOMENTS AND COMMUTATORS OF PROBABILITY MEASURES
MOMENTS AND COMMUTATORS OF PROBABILITY MEASURES
复制标题
概率测度的矩和换向子
DOI：
10.1142/s0219025707002841
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
A. Stan
中科院分区：
文献类型：
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作者：
Luigi Accardi;Hui;A. Stan
设 a0、a- 和 a+ 分别为 ℝd 上概率测度 μ 的保存算子、消灭算子和创建算子。算子 a0 和 [a-, a+] 被证明可以唯一确定 μ 的矩。我们讨论这样的问题：“两个算子族必须满足什么条件，才能保证概率测度的存在，具有任意阶的有限矩，使得其相关的保存算子以及湮灭算子和创建算子之间的交换子是给定的算子族？”对于 d = 1 的情况，这个问题的满意答案是根据 Szego-Jacobi 参数的简单条件获得的。对于多维情况，我们给出了回答这个问题的一些必要条件。对于 ℝ 上的一些经典概率度量，我们还给出了一个表格，其中包含湮灭和创建算子之间相关的保存和交换器。
Let a0, a- and a+ be the preservation, annihilation, and creation operators of a probability measure μ on ℝd, respectively. The operators a0 and [a-, a+] are proven to uniquely determine the moments of μ. We discuss the question: "What conditions must two families of operators satisfy, in order to ensure the existence of a probability measure, having finite moments of any order, so that, its associated preservation operators and commutators between the annihilation and creation operators are the given families of operators?" For the case d = 1, a satisfactory answer to this question is obtained as a simple condition in terms of the Szego–Jacobi parameters. For the multidimensional case, we give some necessary conditions for the answer to this question. We also give a table with the associated preservation and commutator between the annihilation and creation operators, for some of the classic probability measures on ℝ.
DOI：
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发表时间：
2006
期刊：
Quantum Information V
影响因子：
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作者：
Hidetaka Hamada;Tatsuhiro Honda;Gabriela Kohr;Izumi Kubo;Hisashi Yokota;Hidetaka Hamada;Nobuhiro Asai
通讯作者：
Nobuhiro Asai