TY - JOUR
T1 - On clifford analysis for holomorphic mappings
AU - Luna-Elizarrarás, M. E.
AU - Shapiro, M.
AU - Struppa, D. C.
N1 - Publisher Copyright:
© de Gruyter 2014.
PY - 2014/7/1
Y1 - 2014/7/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84925357508&partnerID=8YFLogxK
U2 - 10.1515/advgeom-2014-0003
DO - 10.1515/advgeom-2014-0003
M3 - Artículo
SN - 1615-715X
VL - 14
SP - 413
EP - 426
JO - Advances in Geometry
JF - Advances in Geometry
IS - 3
ER -