TY - JOUR
T1 - On the φ -Hyperderivative of the ψ -Cauchy-Type Integral in Clifford Analysis
AU - Abreu Blaya, Ricardo
AU - Bory Reyes, Juan
AU - Adán, Alí Guzmán
AU - Kähler, Uwe
N1 - Publisher Copyright:
© 2016, Springer-Verlag Berlin Heidelberg.
PY - 2017/3/1
Y1 - 2017/3/1
N2 - 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.
AB - 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.
KW - Cauchy-type integral
KW - Clifford analysis
KW - Hyperderivative
KW - Hyperholomorphy
UR - http://www.scopus.com/inward/record.url?scp=85014816912&partnerID=8YFLogxK
U2 - 10.1007/s40315-016-0172-0
DO - 10.1007/s40315-016-0172-0
M3 - Artículo
SN - 1617-9447
VL - 17
SP - 101
EP - 119
JO - Computational Methods and Function Theory
JF - Computational Methods and Function Theory
IS - 1
ER -