Martinelli-Bochner type formulae in complex Clifford analysis
type: Item
instance of: scholarly article
title: Martinelli-Bochner type formulae in complex Clifford analysis
zbMATH Open document ID: 0651.30027
DOI: 10.4171/ZAA/230
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1987-01-01T00:00:00Z
review text: Let \({\mathcal A}\) be the Clifford algebra over \({\mathbb{C}}^ m,\) ẕ\(=\underline x+i\underline y\in {\mathbb{C}}^ m \)and \(D_ x=\sum^{m}_{i=1}e_ j\partial /\partial x_ j,\) \(D_ y\) analogously defined, where \(\{e_ 1,...,e_ m\}\) is an orthonormal base of \({\mathbb{C}}^ m.\) Using the kernel \(\omega_{2m}E(\underline z)=- \underline z\quad *| \underline z|^{-2m}\) \((\omega_{2m}\) is the area of \(S_{2m-1}\), * means complex conjugation) the author proves a very general theorem of Bochner-Martinelli type for solutions of \((D_ x+iD_ y)f=0\), f continuously differentiable with respect to \(x_ j\), \(y_ j\) in a domain in \({\mathbb{C}}^ m.\) In various special cases this gives generalizations of known theorems and interesting connections to several parts of complex variable theory.
Mathematics Subject Classification ID: 30G35
Mathematics Subject Classification ID: 30E20
Mathematics Subject Classification ID: 32A25
zbMATH DE Number: 4061617
zbMATH Keywords: Clifford analysis
zbMATH Keywords: Bochner-Martinelli theorems
author: Frank Sommen
reviewed by: Klaus Habetha
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/zaa/230
OpenAlex ID: W2564773118
description: scientific article; zbMATH DE number 4061617