论文标题
无限尺寸分数泊松测量的生物表达方法
A biorthogonal approach to the infinite dimensional fractional Poisson measure
论文作者
论文摘要
在本文中，我们使用生物三相方法来分析无限的尺寸分数泊松度量$π_σ^β$，$ 0 <β\ leq1 $，在Schwartz测试功能空间$ \ MATHCAL {D}'$上。复杂值函数的Hilbert Space $ l^{2}（π_σ^β）$是用广义的appell polyenmials $ \ mathbb {p}^{σ，β，α} $相关的系统的系统来描述的。 $ c_ {n}^{σ，β}（\ cdot）$，$ n \ in \ mathbb {n} _ {0} $，可以用第一和第二类的stirling ocersions表示，也可以用第一和第二种的stirling operator表示。与系统$ \ mathbb {p}^{σ，β，α} $相关联，有一个通用的双appell系统$ \ mathbb {q}^{σ，β，β，α} $，是biiorthogonal to $ \ m mathbb {p}^{p}^{σ，β，β，α} $。与度量$π_σ^β$相关的测试和广义函数空间完全以整体变换为整个函数完全表征。
In this paper we use a biorthogonal approach to the analysis of the infinite dimensional fractional Poisson measure $π_σ^β$, $0<β\leq1$, on the dual of Schwartz test function space $\mathcal{D}'$. The Hilbert space $L^{2}(π_σ^β)$ of complex-valued functions is described in terms of a system of generalized Appell polynomials $\mathbb{P}^{σ,β,α}$ associated to the measure $π_σ^β$. The kernels $C_{n}^{σ,β}(\cdot)$, $n\in\mathbb{N}_{0}$, of the monomials may be expressed in terms of the Stirling operators of the first and second kind as well as the falling factorials in infinite dimensions. Associated to the system $\mathbb{P}^{σ,β,α}$, there is a generalized dual Appell system $\mathbb{Q}^{σ,β,α}$ that is biorthogonal to $\mathbb{P}^{σ,β,α}$. The test and generalized function spaces associated to the measure $π_σ^β$ are completely characterized using an integral transform as entire functions.
