Normal families of bicomplex meromorphic functions
Volume 103 / 2012
Annales Polonici Mathematici 103 (2012), 303-317
MSC: Primary 30G, 30G35, 30D30; Secondary 32A, 32A30.
DOI: 10.4064/ap103-3-6
Abstract
We introduce the extended bicomplex plane $\overline{\mathbb{T}}$, its geometric model: the bicomplex Riemann sphere, and the bicomplex chordal metric that enables us to talk about convergence of sequences of bicomplex meromorphic functions. Hence the concept of normality of a family of bicomplex meromorphic functions on bicomplex domains emerges. Besides obtaining a normality criterion for such families, the bicomplex analog of the Montel theorem for meromorphic functions and the fundamental normality tests for families of bicomplex holomorphic functions and bicomplex meromorphic functions are also obtained.
