Criteria for monogenicity of Clifford algebra-valued functions on fractal domains
type: Item
instance of: scholarly article
title: Criteria for monogenicity of Clifford algebra-valued functions on fractal domains
zbMATH Open document ID: 1206.30063
author: Ricardo Abreu-Blaya
author: Juan Bory-Reyes
published in: Archiv der Mathematik
publication date: 2010-10-08T00:00:00Z
review text: It is assumed a compact domain \(G\subset\mathbb{R}^{n+1}\) with a fractal boundary \(\Gamma\). The authors consider a \(\text{Cl}_{0,n}\)-valued function \(U\) on \(\overline G\), which is harmonic in \(G\) and Hölder-continuous on \(\Gamma\). By using the box dimension of the boundary for Hölder-continuous \(\text{Cl}_{0,n}\)-valued functions a Clifford-Cauchy transform can be defined. This is done by the authors in former papers. Necessary and sufficient conditions for the monogenicity of \(U\) in terms of the values of the fractal boundary is given. This result generalizes a corresponding one obtained by the first author for Ahlfors-David boundaries.
Mathematics Subject Classification ID: 30G35
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 5797836
zbMATH Keywords: Clifford analysis
zbMATH Keywords: Cauchy-Riemann operator
zbMATH Keywords: Cauchy transform
MaRDI profile type: Publication
full work available at URL: s00013-010-0140-2
OpenAlex ID: W2022180956
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DOI: 10.1007/S00013-010-0140-2
description: scientific article; zbMATH DE number 5797836