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

Daniel Alpay (editor) (2006) Wavelets, Multiscale systems and Hypercomplex Analysis, Springer, ISBN 9783764375881 .
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).
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.
Sorin D. Gal (2004) Introduction to the Geometric Function theory of Hypercomplex variables, Nova Science Publishers, ISBN 1-59033-398-5.
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.
Birkhauser Mathematics (2011) Hypercomplex Analysis and Applications, series with editors Irene Sabadini and Franciscus Sommen.
Irene Sabadini & Michael V. Shapiro & F. Sommen (editors) (2009) Hypercomplex Analysis, Birkhauser ISBN 978-3-7643-9892-7.
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".
Roman Lavika (2011) Hypercomplex Analysis: Selected Topics (Habilitation Thesis) Charles University in Prague.