On Clifford analysis for holomorphic mappings

Autor:	Maria Elena Luna-Elizarrarás, Michael Shapiro, Daniele C. Struppa
Rok vydání:	2014
Předmět:	Algebra Classification of Clifford algebras Mathematics::Complex Variables Clifford algebra Several complex variables Holomorphic function Analyticity of holomorphic functions Landau's constants Geometry and Topology Clifford analysis Identity theorem Mathematics
Zdroj:	Advances in Geometry. 14:413-426
ISSN:	1615-7168 1615-715X
DOI:	10.1515/advgeom-2014-0003
Popis:	In the classical theory of several complex variables, holomorphic mappings are just n-tuples of holomorphic functions in m variables, with arbitrary n andm, 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.
Databáze:	OpenAIRE
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