Fueter's theorem in discrete Clifford analysis

被引：0

作者：

De Ridder, Hilde ^{[1
]}

Sommen, Frank ^{[1
]}

机构：

[1] Univ Ghent, Dept Math Anal, Fac Engn & Architecture, Bldg S22,Galglaan 2, B-9000 Ghent, Belgium

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2016年 / 39卷 / 07期

基金：

比利时弗兰德研究基金会;

关键词：

discrete Clifford analysis; axial monogenicity; Fueter theorem;

D O I：

10.1002/mma.3612

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we discretize techniques for the construction of axially monogenic functions to the setting of discrete Clifford analysis. Wherefore, we work in the discrete Hermitian Clifford setting, where each basis vector e(j) is split into a forward and backward basis vector: ej=ej++ej-. We prove a discrete version of Fueter's theorem in odd dimension by showing that for a discrete monogenic function f((0),(1)) left-monogenic in two variables (0) and (1) and for a left-monogenic P-k(), the m-dimensional function k+m-12f(01)Pk() is in itself left monogenic, that is, a discrete function in the kernel of the discrete Dirac operator. Closely related, we consider a Vekua-type system for the construction of axially monogenic functions. We consider some explicit examples: the discrete axial-exponential functions and the discrete Clifford-Hermite polynomials. Copyright (c) 2015 John Wiley & Sons, Ltd.

引用

页码：1908 / 1920

页数：13

共 15 条

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