In this paper, we unify techniques of Pascal white noise analysis and harmonic analysis on configuration spaces establishing relations between the main structures of both ones. Fix a Random measure [Formula: see text] on a Riemannian manifold [Formula: see text], we construct on the space of finite compound configuration space [Formula: see text] the so-called Lebesgue–Pascal measure [Formula: see text] and as a consequence we obtain the Pascal measure [Formula: see text] on the compound configuration space [Formula: see text]. Next, the natural realization of the symmetric Fock space over [Formula: see text] as the space [Formula: see text] leads to the unitary isomorphism [Formula: see text] between the space [Formula: see text] and [Formula: see text]. Finally, in the first application we study some algebraic products, namely, the Borchers product on the Fock space, the Wick product on the Pascal space, and the ⋆-convolution on the Lebesgue–Pascal space and we prove that the Pascal white noise analysis and harmonic analysis are related through an equality of operators involving [Formula: see text]. The second application is devoted to solve the implementation problem.

中文翻译：

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配置空间和应用的帕斯卡白噪声谐波分析

在本文中，我们统一了帕斯卡白噪声分析和谐波分析技术，对配置空间建立了两者的主要结构之间的关系。在黎曼流形[公式：见文]上固定一个随机测度[公式：见文]，我们在有限复合配置空间[公式：见文]的空间上构造所谓的勒贝格-帕斯卡测度[公式：见文] ]，因此我们在复合配置空间 [公式：参见文本] 上获得了帕斯卡度量 [公式：参见文本]。接下来，将[公式：见文]上的对称福克空间自然实现为空间[公式：见文]导致空间[公式：见文]和[公式：见文]之间的酉同构[公式：见文]见正文]。最后，在第一个应用程序中，我们研究了一些代数产品，即，Fock 空间上的 Borchers 乘积、Pascal 空间上的 Wick 乘积和 Lebesgue-Pascal 空间上的 ⋆-卷积，我们证明了 Pascal 白噪声分析和谐波分析通过涉及 [公式：见正文]。第二个应用程序致力于解决实现问题。