Some elements of a theory of multidimensional complex variables. I: General theory
type: Item
instance of: scholarly article
title: Some elements of a theory of multidimensional complex variables. I: General theory
zbMATH Open document ID: 0696.30049
DOI: 10.1016/0016-0032(89)90024-0
author: E. Dale Martin
published in: Journal of the Franklin Institute
publication date: 1989-01-01T00:00:00Z
review text: The author considers the algebra over the complex numbers with basis 1, j, \(j^ 2\), assuming \(j^ 3=-1\), generalizations to higher dimensions are given. Relations between the coordinates for different bases are dealt with, especially used are cylindrical and spherical coordinates. Differentiable functions in the usual sense are called analytic, the corresponding Cauchy-Riemann-equations are calculated. These are also considered for the different bases. The real and imaginary parts of such functions are harmonic vectors if written down within the right base. There are no integral theorems (which exist).
Mathematics Subject Classification ID: 30G35
Mathematics Subject Classification ID: 31B05
zbMATH DE Number: 4140139
zbMATH Keywords: function theory in algebras
zbMATH Keywords: cyclic algebras
zbMATH Keywords: Cauchy-Riemann-equations
reviewed by: Klaus Habetha
MaRDI profile type: Publication
full work available at URL: 0016-0032(89)90024-0
OpenAlex ID: W2082023197
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description: scientific article; zbMATH DE number 4140139