On the hyperderivatives of dirac-hyperholomorphic functions of clifford analysis

M. Elena Luna-Elizarrarás, Marco A. Macías-Cedeño, Michael Shapiro

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Abstract

© 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.
Original languageAmerican English
Title of host publicationOn the hyperderivatives of dirac-hyperholomorphic functions of clifford analysis
Pages179-195
Number of pages159
ISBN (Electronic)9783034803458
StatePublished - 1 Jan 2012
EventOperator Theory: Advances and Applications -
Duration: 1 Jan 2012 → …

Publication series

NameOperator Theory: Advances and Applications
Volume220
ISSN (Print)0255-0156

Conference

ConferenceOperator Theory: Advances and Applications
Period1/01/12 → …

Fingerprint

Clifford Analysis
Cauchy
Paul Adrien Maurice Dirac
Dirac Operator
Cauchy-type Integral
Hyperplane
Zero
Operator

Cite this

Luna-Elizarrarás, M. E., Macías-Cedeño, M. A., & Shapiro, M. (2012). On the hyperderivatives of dirac-hyperholomorphic functions of clifford analysis. In On the hyperderivatives of dirac-hyperholomorphic functions of clifford analysis (pp. 179-195). (Operator Theory: Advances and Applications; Vol. 220).
Luna-Elizarrarás, M. Elena ; Macías-Cedeño, Marco A. ; Shapiro, Michael. / On the hyperderivatives of dirac-hyperholomorphic functions of clifford analysis. On the hyperderivatives of dirac-hyperholomorphic functions of clifford analysis. 2012. pp. 179-195 (Operator Theory: Advances and Applications).
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Luna-Elizarrarás, ME, Macías-Cedeño, MA & Shapiro, M 2012, On the hyperderivatives of dirac-hyperholomorphic functions of clifford analysis. in 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.

On the hyperderivatives of dirac-hyperholomorphic functions of clifford analysis. 2012. p. 179-195 (Operator Theory: Advances and Applications; Vol. 220).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Luna-Elizarrarás ME, Macías-Cedeño MA, Shapiro M. On the hyperderivatives of dirac-hyperholomorphic functions of clifford analysis. In On the hyperderivatives of dirac-hyperholomorphic functions of clifford analysis. 2012. p. 179-195. (Operator Theory: Advances and Applications).