Geometry and Identity Theorems for Bicomplex Functions and Functions of a Hyperbolic Variable

Authors

Maria Elena Luna-Elizarrarás, HIT - Holon Institute of Technology
Marco Panza, Chapman UniversityFollow
Michael Shapiro, HIT - Holon Institute of Technology
Daniele Carlo Struppa, Chapman UniversityFollow

Document Type

Article

Publication Date

5-14-2020

Abstract

In this paper we prove that D-holomorphic functions satisfy an unexpected limited version of the identity theorem. We will offer two distinct proofs that shed some light on the geometry of D. Since hyperbolic numbers are naturally embedded in the four-dimensional algebra of bicomplex numbers, we use our approach to state and prove an identity theorem for the bicomplex case as well.

Comments

This article was originally published in Milan Journal of Mathematics, volume 88, in 2020. https://doi.org/10.1007/s00032-020-00313-8

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Recommended Citation

Luna–Elizarrarás, M.E., Panza, M., Shapiro, M. et al. Geometry and Identity Theorems for Bicomplex Functions and Functions of a Hyperbolic Variable. Milan J. Math. 88, 247–261 (2020). https://doi.org/10.1007/s00032-020-00313-8

Peer Reviewed

1

Copyright

Springer