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# Cauchy integral formulae in quaternionic hermitean clifford analysis

(2012) 6(5). p.971-985
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Abstract
The theory of complex Hermitean Clifford analysis was developed recently as a refinement of Euclidean Clifford analysis; it focusses on the simultaneous null solutions, called Hermitean monogenic functions, of two Hermitean Dirac operators constituting a splitting of the traditional Dirac operator. In this function theory, the fundamental integral representation formulae, such as the Borel–Pompeiu and the Clifford–Cauchy formula have been obtained by using a (2 × 2) circulant matrix formulation. In the meantime, the basic setting has been established for so–called quaternionic Hermitean Clifford analysis, a theory centered around the simultaneous null solutions, called q–Hermitean monogenic functions, of four Hermitean Dirac operators in a quaternionic Clifford algebra setting. In this paper we address the problem of establishing a quaternionic Hermitean Clifford–Cauchy integral formula, by following a (4 × 4) circulant matrix approach.
Keywords
Cauchy integral formula., quaternionic Hermitean Clifford analysis

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## Citation

Chicago
Abreu Blaya, Ricardo, Juan Bory Reyes, Fred Brackx, Hennie De Schepper, and Franciscus Sommen. 2012. “Cauchy Integral Formulae in Quaternionic Hermitean Clifford Analysis.” Complex Analysis and Operator Theory 6 (5): 971–985.
APA
Abreu Blaya, Ricardo, Bory Reyes, J., Brackx, F., De Schepper, H., & Sommen, F. (2012). Cauchy integral formulae in quaternionic hermitean clifford analysis. COMPLEX ANALYSIS AND OPERATOR THEORY, 6(5), 971–985.
Vancouver
1.
Abreu Blaya R, Bory Reyes J, Brackx F, De Schepper H, Sommen F. Cauchy integral formulae in quaternionic hermitean clifford analysis. COMPLEX ANALYSIS AND OPERATOR THEORY. 2012;6(5):971–85.
MLA
Abreu Blaya, Ricardo, Juan Bory Reyes, Fred Brackx, et al. “Cauchy Integral Formulae in Quaternionic Hermitean Clifford Analysis.” COMPLEX ANALYSIS AND OPERATOR THEORY 6.5 (2012): 971–985. Print.
```@article{3032976,
abstract     = {The theory of complex Hermitean Clifford analysis was developed recently as a refinement of Euclidean Clifford analysis; it focusses on the simultaneous null solutions, called Hermitean monogenic functions, of two Hermitean Dirac operators constituting a splitting of the traditional Dirac operator. In this function theory, the fundamental integral representation formulae, such as the Borel--Pompeiu and the Clifford--Cauchy formula have been obtained by using a (2 {\texttimes} 2) circulant matrix formulation. In the meantime, the basic setting has been established for so--called quaternionic Hermitean Clifford analysis, a theory centered around the simultaneous null solutions, called q--Hermitean monogenic functions, of four Hermitean Dirac operators in a quaternionic Clifford algebra setting. In this paper we address the problem of establishing a quaternionic Hermitean Clifford--Cauchy integral formula, by following a (4 {\texttimes} 4) circulant matrix approach.},
author       = {Abreu Blaya, Ricardo and Bory Reyes, Juan  and Brackx, Fred and De Schepper, Hennie and Sommen, Franciscus},
issn         = {1661-8254},
journal      = {COMPLEX ANALYSIS AND OPERATOR THEORY},
keyword      = {Cauchy integral formula.,quaternionic Hermitean Clifford analysis},
language     = {eng},
number       = {5},
pages        = {971--985},
title        = {Cauchy integral formulae in quaternionic hermitean clifford analysis},
url          = {http://dx.doi.org/10.1007/s11785-011-0168-8},
volume       = {6},
year         = {2012},
}

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