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