Treffer: n-Dimensional hyperbolic complex numbers: \(n\)-dimensional hyperbolic complex numbers

Title:
n-Dimensional hyperbolic complex numbers: \(n\)-dimensional hyperbolic complex numbers
Authors:
Sorin G. Gal, Paul Fjelstad
Source:
Advances in Applied Clifford Algebras. 8:47-68
Publisher Information:
Springer Science and Business Media LLC, 1998.
Publication Year:
1998
Subject Terms:
Functions of hypercomplex variables and generalized variables, 0103 physical sciences, JFM 62.1122.03, 01 natural sciences
Document Type:
Fachzeitschrift Article
File Description:
application/xml
Language:
English
ISSN:
1661-4909
0188-7009
DOI:
10.1007/bf03041925
Access URL:
https://link.springer.com/article/10.1007/BF03041925
Rights:
Springer TDM
Accession Number:
edsair.doi.dedup.....a7ebc5f9d3e17e960d4413d0b743294f
Database:
OpenAIRE

Weitere Informationen

In this contribution is deduced a generalisation of the 2-dimensional complex number system. The construction of a hyperbolic basis is one of the main topics in this paper. By the aid of this basis the authors succeed in a nice description of an \(n\)-dimensional direct product ring of reals. Problems which appear with zero divisors where explained in detail. Elementary functions similar to the ``elliptic'' case were introduced. Finally, analogues to the Cauchy-Riemann equations were studied. The notation of a hyperbolic conformal mapping is given and some examples strike the meaning of these considerations. Basic results were obtained in the paper: \textit{A. Duranona Vedia} and \textit{J. C. Vignaux}: On the theory of functions of a hyperbolic complex variable (in Spain) Univ. Nac. La Plata (Argentina), Publ. Fac. Ci. Fisicomat. Contr. 104, 139-183 (1935; JFM 62.1122.03).