The Bessel-Clifford Function Associated to the Cayley-Laplace Operator

被引:0
作者
Eelbode, David [1 ]
机构
[1] Univ Antwerp, Dept Math, Midddelheimlaan 1, B-2020 Antwerp, Belgium
关键词
Cayley-Laplace operator; Matrix variables; Special functions; Binomial polynomials; Nayarana numbers; GEOMETRY; SPACE;
D O I
10.1007/s00006-024-01351-w
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper the Cayley-Laplace operator Delta xu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta _{xu}$$\end{document} is considered, a rotationally invariant differential operator which can be seen as a generalisation of the classical Laplace operator for functions depending on wedge variables Xab\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X_{ab}$$\end{document} (the minors of a matrix variable). We will show that the Bessel-Clifford function appears naturally in the framework of two-wedge variables, and explain how this function somehow plays the role of the exponential function in the framework of Grassmannians. This will be used to obtain a generalisation of the series expansion for the Newtonian potential, and to investigate a new kind of binomial polynomials related to Nayarana numbers.
引用
收藏
页数:20
相关论文
共 15 条
[11]  
Mihir T., 2018, Int. J. Stat. Appl. Math, V3, P492
[12]  
Narayana T.V., 1979, Mathematical Expositions, V23, P100
[14]  
SUMITOMO T, 1991, OSAKA J MATH, V28, P1017
[15]   THE HIGGS ALGEBRA AS A QUANTUM DEFORMATION OF SU(2) [J].
ZHEDANOV, AS .
MODERN PHYSICS LETTERS A, 1992, 7 (06) :507-512