On the φ -Hyperderivative of the ψ -Cauchy-Type Integral in Clifford Analysis

Abstract:

The aim of this paper is to introduce, in the framework of Clifford analysis, the notions of φ-hyperdifferentiability and φ-hyperderivability for ψ-hyperholomorphic functions where (φ, ψ) are two arbitrary orthogonal bases (called structural sets) of a Euclidean space. In this study we will also show how to exchange the integral sign and the φ-hyperderivative of the ψ-Cliffordian Cauchy-type integral. Thereby, we generalize, in a natural way, the corresponding quaternionic antecedent as well as the standard Clifford predecessor.

Año de publicación:

2017

Keywords:

• Hyperholomorphy
• Clifford analysis
• Hyperderivative
• Cauchy-type integral

Fuente:

scopus