Bicomplex holomorphic functional calculus

Normal Families of Bicomplex Holomorphic Functions

In this article, we introduce the concept of normal families of bicomplex holomorphic functions to obtain a bicomplex Montel theorem. Moreover, we give a general definition of Fatou and Julia sets for bicomplex polynomials and we obtain a characterization of bicomplex Fatou and Julia sets in terms of Fatou set, Julia set and filled-in Julia set of one complex variable. Some 3D visual examples o...

Holomorphic Functional Calculus and Some Applications

In this note, we present some applications of complex analysis to functional analysis and operator theory. We will focus on some basic facts of holomorphic functional calculus and its applications to analyze the spectrum of operators.

Multicentric Holomorphic Calculus

The Invariant Variational Bicomplex

We establish a group-invariant version of the variational bicomplex that is based on a general moving frame construction. The main application is an explicit group-invariant formula for the Euler-Lagrange equations of an invariant variational problem.

Bicomplex algebra and function theory

This treatise investigates holomorphic functions defined on the space of bicomplex numbers introduced by Segre. The theory of these functions is associated with Fueter’s theory of regular, quaternionic functions. The algebras of quaternions and bicomplex numbers are developed by making use of so-called complex pairs. Special attention is paid to singular bicomplex numbers that lack an inverse. ...