Annihilators for harmonic differential forms via Clifford analysis
type: Item
instance of: scholarly article
title: Annihilators for harmonic differential forms via Clifford analysis
zbMATH Open document ID: 1267.30102
author: Ricardo Abreu-Blaya
author: Juan Bory-Reyes
author: Richard Delanghe
author: Frank Sommen
published in: Advances in Applied Clifford Algebras
publication date: 2011-10-18T00:00:00Z
review text: The authors completely describe the annihilators of harmonic differential forms using Clifford algebras and the methods introduced by the authors in [Adv. Appl. Clifford Algebr. 17, No. 4, 589--610 (2007; Zbl 1134.30336)]. Their tools are different from methods used by \textit{B. Gustafsson} and \textit{D. Khavinson} [J. Math. Sci., New York 92, No. 1, 3600--3612 (1998); translation from Zap. Nauchn. Semin. POMI 232, 90--108 (1996; Zbl 0891.30029)]. The idea of using Clifford algebras is coming from the result that there exists a one-to-one correspondence between harmonic differential forms in the sense of Hodge and harmonic Clifford valued multivector fields (see [\textit{R. Abreu-Blaya, J. Bory-Reyes, R. Delanghe} and \textit{F. Sommen}, Bull. Belg. Math. Soc. - Simon Stevin 11, No. 1, 95--110 (2004; Zbl 1063.30045)]).
Mathematics Subject Classification ID: 30G35
zbMATH DE Number: 5959939
zbMATH Keywords: harmonic forms
zbMATH Keywords: Clifford analysis
zbMATH Keywords: duality theory
zbMATH Keywords: Dirac operator
MaRDI profile type: Publication
full work available at URL: s00006-010-0268-y
OpenAlex ID: W2005290630
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DOI: 10.1007/S00006-010-0268-Y
description: scientific article; zbMATH DE number 5959939