### Abstract

Original language | American English |
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Title of host publication | On the hyperderivatives of dirac-hyperholomorphic functions of clifford analysis |

Pages | 179-195 |

Number of pages | 159 |

ISBN (Electronic) | 9783034803458 |

State | Published - 1 Jan 2012 |

Event | Operator Theory: Advances and Applications - Duration: 1 Jan 2012 → … |

### Publication series

Name | Operator Theory: Advances and Applications |
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Volume | 220 |

ISSN (Print) | 0255-0156 |

### Conference

Conference | Operator Theory: Advances and Applications |
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Period | 1/01/12 → … |

### Fingerprint

### Cite this

*On the hyperderivatives of dirac-hyperholomorphic functions of clifford analysis*(pp. 179-195). (Operator Theory: Advances and Applications; Vol. 220).

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*On the hyperderivatives of dirac-hyperholomorphic functions of clifford analysis.*Operator Theory: Advances and Applications, vol. 220, pp. 179-195, Operator Theory: Advances and Applications, 1/01/12.

**On the hyperderivatives of dirac-hyperholomorphic functions of clifford analysis.** / Luna-Elizarrarás, M. Elena; Macías-Cedeño, Marco A.; Shapiro, Michael.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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

PY - 2012/1/1

Y1 - 2012/1/1

N2 - © 2012 Springer Basel AG. 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 - © 2012 Springer Basel AG. 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.

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84956483131&origin=inward

UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=84956483131&origin=inward

M3 - Conference contribution

SN - 9783034803458

T3 - Operator Theory: Advances and Applications

SP - 179

EP - 195

BT - On the hyperderivatives of dirac-hyperholomorphic functions of clifford analysis

ER -