基于拟单性原理的离散变量超复多项式类
Classes of hypercomplex polynomials of discrete variable based on the quasi-monomiality principle
摘要：
为了在离散超复变量的背景下推导出准单性公式，人们将通过签名$(0,n)$的Clifford代数结构合并具有Lie代数对称性的阴影演算框架。指数母函数（{ \bf EGF}）携带{ \it continuum} Dirac算子$D=\sum_{j=1}^n\e_j\partial_{x_j}$以及作用在格$h\BZ^n$上的升降算子的李代数表示，用于导出相应的离散变量超复多项式作为Clifford向量值多项式空间上的Appell集.一些特殊的例子，如超复杂版本的下降因子和Poisson-Charlier多项式的介绍。从插值理论和积分变换的观点讨论了某些应用。
英文摘要：
With the aim of derive a quasi-monomiality formulation in the context of discrete hypercomplex variables, one will amalgamate through a Clifford-algebraic structure of signature $(0,n)$ the umbral calculus framework with Lie-algebraic symmetries. The exponential generating function ({\bf EGF}) carrying the {\it continuum} Dirac operator $D=\sum_{j=1}^n\e_j\partial_{x_j}$ together with the Lie-algebraic representation of raising and lowering operators acting on the lattice $h\BZ^n$ is used to derive the corresponding hypercomplex polynomials of discrete variable as Appell sets with membership on the space Clifford-vector-valued polynomials. Some particular examples concerning this construction such as the hypercomplex versions of falling factorials and the Poisson-Charlier polynomials are introduced. Certain applications from the view of interpolation theory and integral transforms are also discussed.
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