Holomorphic synthesis of monogenic functions of several quaternionic variables
type: Item
instance of: scholarly article
title: Holomorphic synthesis of monogenic functions of several quaternionic variables
zbMATH Open document ID: 0962.30027
DOI: 10.1007/BF02791133
author: V. P. Palamodov
published in: Journal d'Analyse Mathématique
publication date: 1999-12-19T00:00:00Z
review text: Let \(\Sigma\) be the variety of complex structures \(\sigma\) in the quaternions \(H\) which make \(H\) isomorphic to \(C^{2}\) and which are consistent with the metric and orientation in \(H\). It is proved that \(\Sigma\) is isomorphic to the manifold of all proper ideals in the complexified quaternion algebra \(H_{C}\). This enables the author to find a representation for polymonogenic functions in \(H\) by integrating over \(\Sigma\). Here polymonogenic means functions which are monogenic to each of several quaternionic variables. See also \textit{W. W. Adams, P. Loustaunau, V. P. Palamodov} and \textit{D. C. Struppa} in Ann. Inst. Fourier 47, No. 2, 623-640 (1997; Zbl 0974.32005).
reviewed by: Klaus Habetha
Mathematics Subject Classification ID: 30G35
zbMATH DE Number: 1369960
zbMATH Keywords: quaternionic analysis
zbMATH Keywords: polymonogenic functions
zbMATH Keywords: complex structures in quaternions
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02791133
OpenAlex ID: W2063697244
description: scientific article; zbMATH DE number 1369960