TY - GEN
T1 - On the hyperderivatives of dirac-hyperholomorphic functions of clifford analysis
AU - Luna-Elizarrarás, M. Elena
AU - Macías-Cedeño, Marco A.
AU - Shapiro, Michael
N1 - Publisher Copyright:
© 2012 Springer Basel AG.
PY - 2012
Y1 - 2012
N2 - In the context of Clifford analysis, considering the Cauchy-Riemann and Dirac operators one has that any Dirac-hyperholomorphic function is also Cauchy-Riemann-hyperholomorphic, but its hyperderivative in the Cauchy- Riemann sense is always zero, so these functions can be thought of as “constants” for the Cauchy-Riemann operator. It turns out that it is possible to give another kind of hyperderivatives “consistent” with the Dirac operator, but there are several of them. We focus in detail on one of these hyperderivatives and develop also the notion of (n – 1)-dimensional directional hyperderivative along a hyperplane. As in the previous works, an application to the Cliffordian-Cauchy-type integral proves to be instructive.
AB - In the context of Clifford analysis, considering the Cauchy-Riemann and Dirac operators one has that any Dirac-hyperholomorphic function is also Cauchy-Riemann-hyperholomorphic, but its hyperderivative in the Cauchy- Riemann sense is always zero, so these functions can be thought of as “constants” for the Cauchy-Riemann operator. It turns out that it is possible to give another kind of hyperderivatives “consistent” with the Dirac operator, but there are several of them. We focus in detail on one of these hyperderivatives and develop also the notion of (n – 1)-dimensional directional hyperderivative along a hyperplane. As in the previous works, an application to the Cliffordian-Cauchy-type integral proves to be instructive.
KW - Cauchy-type integrals
KW - Clifford analysis
KW - Dirac operator
KW - Hyperderivative
UR - http://www.scopus.com/inward/record.url?scp=84956483131&partnerID=8YFLogxK
U2 - 10.1007/978-3-0348-0346-5_11
DO - 10.1007/978-3-0348-0346-5_11
M3 - Contribución a la conferencia
SN - 9783034803458
T3 - Operator Theory: Advances and Applications
SP - 179
EP - 195
BT - Recent Progress in Operator Theory and Its Applications
A2 - Ball, Joseph A.
A2 - Helton, J. William
A2 - Curto, Raúl E.
A2 - Grudsky, Sergei M.
A2 - Quiroga-Barranco, Raúl
A2 - Vasilevski, Nikolai L.
PB - Springer International Publishing
T2 - 20th International Workshop on Operator Theory and Applications, IWOTA 2009
Y2 - 21 September 2009 through 25 September 2009
ER -