Document Type
Article
Publication Date
2014
Abstract
In the classical theory of several complex variables, holomorphic mappings are just n-tuples of holomorphic functions in m variables, with arbitrary n and m, and no relations between these functions are assumed. Some 30 years ago John Ryan introduced complex, or complexified, Clifford analysis which is, in a sense, the study of certain classes of holomorphic mappings where the components are not independent, and instead obey the relations generated by the Cauchy– Riemann and Dirac-type operators. In this paper, we take a closer look at this theory emphasizing some additional properties that holomorphic mappings satisfy in this context. Our attention is mostly restricted to the case of low dimensions where it is possible to identify new and interesting properties and to single out the special role played by bicomplex analysis.
Recommended Citation
Luna-Elizarrarás, M. E., Shapiro, M. M., & Struppa, D. C. (2014). On Clifford analysis for holomorphic mappings. Advances In Geometry, 14(3), 413-426. doi:10.1515/advgeom-2014-0003
Peer Reviewed
1
Copyright
de Gruyter
Comments
This article was originally published in Advances in Geometry, volume 14, issue 3, in 2014. DOI: 10.1515/advgeom-2014-0003