广西师范大学学报(自然科学版) ›› 2015, Vol. 33 ›› Issue (4): 73-80.doi: 10.16088/j.issn.1001-6600.2015.04.013

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Dunkl-Clifford分析框架下的Hermite多项式

李珊珊1, 费铭岗2   

  1. 1.西南民族大学计算机科学与技术学院,四川成都610041;
    2.电子科技大学数学科学学院,四川成都611731
  • 收稿日期:2015-03-16 出版日期:2015-12-25 发布日期:2018-09-21
  • 通讯作者: 李珊珊(1980—),女,四川成都人,西南民族大学讲师。E-mail: ssrubyli@163.com
  • 基金资助:
    国家自然科学基金资助项目(11301054);四川省应用基础计划资助项目(2013JY0180);西南民族大学中央高校基金资助项目(2015NZYQN27)

Hermite Polynomials Related to the Dunkl-Clifford Analysis

LI Shan-shan1, FEI Ming-gang2   

  1. 1. College of Computer Science and Technology, Southwest University for Nationalities,Chengdu Sicuan 610041, China;
    2. School of Mathematical Sciences, University of Electronic Scienceand Technology of China, Chengdu Sicuan 611731, China
  • Received:2015-03-16 Online:2015-12-25 Published:2018-09-21

摘要: 本文从纯分析的角度出发,利用Dunkl-Dirac算子的球坐标表示,得到了Dunkl-Clifford分析框架下关于Dunkl算子任意正整数次幂,尤其是奇数次幂下经典Hermite多项式的推广形式。并且作为应用,本文建立了Dunkl-Clifford分析中Hermite多项式所满足的微分方程。

关键词: 反射群, Dunkl-Dirac算子, Hermite多项式

Abstract: In this paper, based on the classical method from Clifford analysis and a spherical representation of Dunkl-Dirac operator, a generalization of the classical Hermite polynomials related to the framework of Dunkl operators is presented. For application, the associated differential equation about Hermite polynomials in Dunkl-Clifford analysis setting is established.

Key words: reflection group, Dunkl-Dirac operator, Hermite polynomials

中图分类号: 

  • O174.22
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