Complex Laplacian and Derivatives of Bicomplex Functions

In this paper we study in detail the theory of bicomplex holomorphy, in the context of the several ways in which bicomplex numbers can be considered. In particular we will show how the notions of bicomplex derivability and bicomplex holomorphy can be interpreted in these different ways, and the cons...

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Bibliographic Details
Published inComplex analysis and operator theory Vol. 7; no. 5; pp. 1675 - 1711
Main Authors Luna-Elizarrarás, M. E., Shapiro, M., Struppa, D. C., Vajiac, A.
Format Journal Article
LanguageEnglish
Published Basel Springer Basel 01.10.2013
Subjects
Analysis
Mathematics
Mathematics and Statistics
Operator Theory
Complex and hyperbolic Laplacians
32A10
30G35
32A30
Bicomplex derivability
Bicomplex differentiability
Bicomplex holomorphic functions
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Summary:In this paper we study in detail the theory of bicomplex holomorphy, in the context of the several ways in which bicomplex numbers can be considered. In particular we will show how the notions of bicomplex derivability and bicomplex holomorphy can be interpreted in these different ways, and the consequences that can be derived.
ISSN:1661-8254
1661-8262
DOI:10.1007/s11785-013-0284-8