Normal Families of Bicomplex Meromorphic Functions

2011/05/23 by K. S. Charak, Charak, K. S., D. Rochon +3 · 1 citation
Mathematics · Earth and Planetary Sciences · #Algebraic and Geometric Analysis #Geophysics and Gravity Measurements #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1105.4580

Abstract

In the present paper, we introduced the extended bicomplex plane \mathbbT, its geometric model: the bicomplex Riemann sphere, and the bicomplex chordal metric that enables us to talk about the convergence of the sequences of bicomplex meromorphic functions. Hence the concept of the 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.

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