Moment functions of higher rank on some types of hypergroups

IF 0.7 3区数学 Q2 MATHEMATICS Semigroup Forum Pub Date : 2023-12-11 DOI:10.1007/s00233-023-10401-x

Żywilla Fechner, Eszter Gselmann, László Székelyhidi

引用次数: 0

Abstract

We consider moment functions of higher order. In our earlier paper, we have already investigated the moment functions of higher order on groups. The main purpose of this work is to prove characterization theorems for moment functions on the multivariate polynomial hypergroups and on the Sturm–Liouville hypergroups. In the first case, the moment generating functions of higher rank are partial derivatives (taken at zero) of the composition of generating polynomials of the hypergroup and functions whose coordinates are given by the formal power series. On Sturm–Liouville hypergroups the moment functions of higher rank are restrictions of even smooth functions that also satisfy certain boundary value problems. The second characterization of moment functions of higher rank on Sturm–Liouville hypergroups is given by means of an exponential family. In this case, the moment functions of higher rank are partial derivatives of an appropriately modified exponential family again taken at zero.

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某些类型超群上的高阶矩函数

我们考虑高阶矩函数。在早先的论文中，我们已经研究了群上的高阶矩函数。这项工作的主要目的是证明多元多项式超群和 Sturm-Liouville 超群上矩函数的特征定理。在第一种情况下，高阶矩生成函数是超群的生成多项式与坐标由形式幂级数给出的函数组成的偏导数（取零）。在 Sturm-Liouville 超群上，高阶矩函数是也满足某些边界值问题的偶平滑函数的限制。Sturm-Liouville 超群上高阶矩函数的第二个特征是通过指数族给出的。在这种情况下，高阶矩函数是一个经过适当修正的指数族的偏导数，再次取值为零。

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来源期刊

Semigroup Forum 数学-数学

CiteScore

1.50

自引率

14.30%

发文量

审稿时长

12 months

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