Hypercomplex analysis
In mathematics, hypercomplex analysis is the extension of real analysis and complex analysis to the study of functions where the argument is a hypercomplex number. The first instance is functions of a quaternion variable, where the argument is a quaternion. A second instance involves functions of a motor variable where arguments are split-complex numbers.
In mathematical physics there are hypercomplex systems called Clifford algebras. The study of functions with arguments from a Clifford algebra is called Clifford analysis.
References
- Irene Sabadini & Michael V. Shapiro Hypercomplex Analysis
- Enrique Ramirez de Arellanon (1998) Operator theory for complex and hypercomplex analysis, American Mathematical Society (Conference proceedings from a meeting in Mexico City in December 1994).
- R. Lavika & A.G. O’ Farrell & I. Short(2007) "Reversible maps in the group of quaternionic Mobius transformations", Mathematical Proceedings of the Cambridge Philosophical Society 143:57–69.
- Roman Lavika (2011) Hypercomplex Analysis: Selected Topics (Habilitation Thesis) Charles University, Prague.
- Birkhauser Mathematics (2011) Hypercomplex Analysis and Applications, series with editors Irene Sabadini and Franciscus Sommen.
- Springer (2012) Advances in Hypercomplex Analysis, eds Sabadini, Sommen, Struppa.
- Chapman University Center of Excellence in Hypercomplex Analysis, includes Daniele Struppa, Chancellor of Chapman University, Chapman faculty, and several "external faculty".
- Daniel Alpay (editor) Wavelets, Multiscale systems and Hypercomplex Analysis.
- Sorin D. Gal (2004) Introduction to the Geometric Function theory of Hypercomplex variables, Nova Science Publishers, ISBN 1-59033-398-5.
- Geoffrey Fox (1949) Elementary Function Theory of a Hypercomplex Variable and the Theory of Conformal Mapping in the Hyperbolic Plane, M.A. thesis, University of British Columbia.