Reproducing kernels of spaces of vector valued monogenics
type: Item
instance of: scholarly article
title: Reproducing kernels of spaces of vector valued monogenics
zbMATH Open document ID: 0885.31009
published in: Advances in Applied Clifford Algebras
publication date: 1998-04-02T00:00:00Z
review text: Let \(Cl( n) \) be a Clifford algebra generated by the vectors \(e_i\) satisfying the relations \(e_ie_j+e_je_i=-2\delta _{ij}\) for \(i,j=1,...,n\). A function \(f:Cl( n) \to Cl( n) \) is called (left) monogenic if \(\partial _xf=\sum_{j=1}^ne_j\partial _xf=0\). The author considers vector valued monogenic functions. For these functions a rich function theory exists, see for example \textit{R. Delanghe, F. Sommen} and \textit{V. Souček} [Clifford algebra and spinor valued functions, Kluwer, Dordrecht (1992; Zbl 0747.53001)]. Without the notation of Clifford algebra they have been studied under the name conjugate harmonic functions. The author studies the question of reproducing kernels for Hilbert spaces of vector valued monogenics. He proves minimum and symmetry properties for these kernels similar to the classical ones. He considers also explicitly the Bergman and the Szegő kernels for the unit ball.
Mathematics Subject Classification ID: 31C05
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 30G35
zbMATH DE Number: 1045722
zbMATH Keywords: Clifford algebra
zbMATH Keywords: monogenic functions
zbMATH Keywords: kernels
zbMATH Keywords: Bergman kernel
zbMATH Keywords: Szegő kernel
zbMATH Keywords: conjugate harmonic functions
zbMATH Keywords: reproducing kernels
zbMATH Keywords: symmetry properties
author: J. Cnops
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1045722