On some categories and functors in the theory of quaternionic Bergman spaces
type: Item
instance of: scholarly article
title: On some categories and functors in the theory of quaternionic Bergman spaces
zbMATH Open document ID: 1187.30045
published in: Advances in Applied Clifford Algebras
publication date: 2009-08-11T00:00:00Z
review text: In \(n\)-dimensional spaces \((n\geq 3)\) the class of holomorphic functions is decribed by so called Möbius transformations. The authors work in the algebra of real quaternions and formulate among other statements some kind of a chain rule with a Möbius transformation between conformally equivalent domains. Then hyperholomorphic Bergman spaces are studied in conformally equivalent domains. The authors use the language of categories and functors. In my opinion it is the only paper where this was done up to now. In such a way the generalized Fueter operator induces a functor between corresponding categories of \(\psi\)-hyperholomorphic Bergman spaces.
Mathematics Subject Classification ID: 30G35
Mathematics Subject Classification ID: 18B30
Mathematics Subject Classification ID: 47B32
zbMATH DE Number: 5593795
zbMATH Keywords: quaternionic analysis
zbMATH Keywords: hyperholomorphic Bergman spaces
zbMATH Keywords: quaternionic Möbius transformations
zbMATH Keywords: categories and functors
author: J. Oscar González-Cervantes
author: M. E. Luna-Elizarrarás
author: M. Shapiro
MaRDI profile type: Publication
full work available at URL: s00006-009-0164-5
OpenAlex ID: W2072511943
DOI: 10.1007/S00006-009-0164-5
description: scientific article; zbMATH DE number 5593795