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Cauchy integral formulae in quaternionic hermitean clifford analysis

Ricardo Abreu Blaya, Juan Bory Reyes, Fred Brackx UGent, Hennie De Schepper UGent and Franciscus Sommen UGent (2012) COMPLEX ANALYSIS AND OPERATOR THEORY. 6(5). p.971-985
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.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
Cauchy integral formula., quaternionic Hermitean Clifford analysis
journal title
COMPLEX ANALYSIS AND OPERATOR THEORY
Complex Anal. Oper. Theory
volume
6
issue
5
pages
971 - 985
Web of Science type
Article
Web of Science id
000310225000001
JCR category
MATHEMATICS
JCR impact factor
0.404 (2012)
JCR rank
221/296 (2012)
JCR quartile
3 (2012)
ISSN
1661-8254
DOI
10.1007/s11785-011-0168-8
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
3032976
handle
http://hdl.handle.net/1854/LU-3032976
date created
2012-10-22 18:42:01
date last changed
2016-12-19 15:43:37
@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},
}

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.