On operators and elementary functions in Clifford analysis
type: Item
instance of: scholarly article
title: On operators and elementary functions in Clifford analysis
zbMATH Open document ID: 0962.30026
DOI: 10.4171/ZAA/886
author: W. Sprössing
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2001-06-04T00:00:00Z
full work available at URL: https://eudml.org/doc/48748
review text: This is an interesting article regarding regular functions in Clifford analysis. Elements from the Clifford algebra of the form \(x_0 + \underline{x}\) with \(x_0 \in\mathbb{R}\) and \(\underline{x} \in\mathbb{R}^n\) are called paravectors. For these paravectors as arguments the classical elementary functions are defined and Moivre's formulas are shown. Then the Cauchy-Fueter operator is decomposed into scalar and spherical terms, and some relations for these operators and paravector valued functions are proved. In the last chapter the Fueter map for regular functions \(\tau_n = \kappa_n\Delta^{\frac{n-1}{2}}\) where \(\kappa_n\) is a normalization factor, is used to get representations and properties for the elementary functions.
reviewed by: Klaus Habetha
Mathematics Subject Classification ID: 30G35
zbMATH DE Number: 1331703
zbMATH Keywords: Clifford analysis
zbMATH Keywords: elementary functions
zbMATH Keywords: Cauchy-Fueter operator
MaRDI profile type: Publication
cites work: Q3310867
cites work: Axial monogenic functions from holomorphic functions
cites work: Q4003806
cites work: Analytische Funktionen einer Quaternionenvariablen
cites work: Q4382291
cites work: Q3751844
cites work: Clifford analysis, biaxial symmetry and pseudoanalytic functions
cites work: Modified clifford analysis
cites work: Modified quaternionic analysis in
cites work: Axially symmetric vector fields and their complex potentials
cites work: Q4857178
cites work: Generalization of Fueter's result to \(\mathbb{R}^{n+1}\)
cites work: Q3252796
cites work: A product and an exponential function in hypercomplex function theory
cites work: Special functions in Clifford analysis and axial symmetry
cites work: Quaternionic analysis
description: scientific article; zbMATH DE number 1331703