TY - GEN
T1 - On the hyperderivatives of moisil-Théodoresco hyperholomorphic functions
AU - Luna-Elizarrarás, M. Elena
AU - Macías-Cedeño, Marco A.
AU - Shapiro, Michael
N1 - Publisher Copyright:
© Springer Basel AG 2011.
PY - 2011
Y1 - 2011
N2 - Any Moisil-Théodoresco-hyperholomorphic function is also Fueterhyperholomorphic, but its hyperderivative is always zero, so these functions can be thought of as "constants" for the Fueter operator. It turns out that it is pobible to give another kind of hyperderivatives "consistent" with the Moisil-Théodoresco operator, but there are several of them. We focus in detail on one of these hyperderivatives and develop also the notion of two-dimensional directional hyperderivative along a plane. As in the previous works, an application to the Cliffordian-Cauchy-type integral proves to be instructive.
AB - Any Moisil-Théodoresco-hyperholomorphic function is also Fueterhyperholomorphic, but its hyperderivative is always zero, so these functions can be thought of as "constants" for the Fueter operator. It turns out that it is pobible to give another kind of hyperderivatives "consistent" with the Moisil-Théodoresco operator, but there are several of them. We focus in detail on one of these hyperderivatives and develop also the notion of two-dimensional directional hyperderivative along a plane. As in the previous works, an application to the Cliffordian-Cauchy-type integral proves to be instructive.
KW - Cauchy-Type Integrals
KW - Hyperderivative
KW - Two-Dimensional Directional Hyperderivative
UR - http://www.scopus.com/inward/record.url?scp=84961364571&partnerID=8YFLogxK
U2 - 10.1007/978-3-0346-0246-4_13
DO - 10.1007/978-3-0346-0246-4_13
M3 - Contribución a la conferencia
SN - 9783034602457
T3 - Trends in Mathematics
SP - 181
EP - 193
BT - Hypercomplex Analysis and Applications
A2 - Sabadini, Irene
A2 - Sommen, Frank
PB - Springer International Publishing
T2 - 7th ISAAC Conference on Hypercomplex Analysis and Applications, 2009
Y2 - 13 July 2009 through 18 July 2009
ER -