Ghent University Academic Bibliography

Advanced

Fischer decompositions in Euclidean and Hermitean Clifford analysis

Fred Brackx UGent, Hennie De Schepper UGent and Vladímir Souček (2010) ARCHIVUM MATHEMATICUM. 46(5). p.301-321
abstract
Euclidean Clifford analysis is a higher dimensional function theory studying so--called monogenic functions, i.e. null solutions of the rotation invariant, vector valued, first order Dirac operator D. In the more recent branch Hermitean Clifford analysis, this rotational invariance has been broken by introducing a complex structure J on Euclidean space and a corresponding second Dirac operator D_J, leading to the system of equations D f = 0 = D_J f expressing so-called Hermitean monogenicity. The invariance of this system is reduced to the unitary group U(n). In this paper we decompose the spaces of homogeneous monogenic polynomials into U(n)-irrucibles involving homogeneous Hermitean monogenic polynomials and we carry out a dimensional analysis of those spaces. Meanwhile an overview is given of so-called Fischer decompositions in Euclidean and Hermitean Clifford analysis.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
Clifford analysis, Fischer decomposition
journal title
ARCHIVUM MATHEMATICUM
Arch. Math.
volume
46
issue
5
pages
301 - 321
ISSN
0044-8753
language
English
UGent publication?
yes
classification
A2
copyright statement
I have transferred the copyright for this publication to the publisher
id
1099690
handle
http://hdl.handle.net/1854/LU-1099690
alternative location
http://dml.cz/handle/10338.dmlcz/141385
date created
2011-01-13 10:20:52
date last changed
2016-12-19 15:46:18
@article{1099690,
  abstract     = {Euclidean Clifford analysis is a higher dimensional function theory studying so--called monogenic functions, i.e. null solutions of the rotation invariant, vector valued, first order Dirac operator D. In the more recent branch Hermitean Clifford analysis, this rotational invariance has been broken by introducing a complex structure J on Euclidean space and a corresponding second Dirac operator D\_J, leading to the system of equations D f = 0 = D\_J f expressing so-called Hermitean monogenicity. The invariance of this system is reduced to the unitary group U(n). In this paper we decompose the spaces of homogeneous monogenic polynomials into U(n)-irrucibles involving homogeneous Hermitean monogenic polynomials and we carry out a dimensional analysis of those spaces. Meanwhile an overview is given of so-called Fischer decompositions in Euclidean and Hermitean Clifford analysis.},
  author       = {Brackx, Fred and De Schepper, Hennie and Sou\v{c}ek, Vlad{\'i}mir},
  issn         = {0044-8753},
  journal      = {ARCHIVUM MATHEMATICUM},
  keyword      = {Clifford analysis,Fischer decomposition},
  language     = {eng},
  number       = {5},
  pages        = {301--321},
  title        = {Fischer decompositions in Euclidean and Hermitean Clifford analysis},
  url          = {http://dml.cz/handle/10338.dmlcz/141385},
  volume       = {46},
  year         = {2010},
}

Chicago
Brackx, Fred, Hennie De Schepper, and Vladímir Souček. 2010. “Fischer Decompositions in Euclidean and Hermitean Clifford Analysis.” Archivum Mathematicum 46 (5): 301–321.
APA
Brackx, Fred, De Schepper, H., & Souček, V. (2010). Fischer decompositions in Euclidean and Hermitean Clifford analysis. ARCHIVUM MATHEMATICUM, 46(5), 301–321.
Vancouver
1.
Brackx F, De Schepper H, Souček V. Fischer decompositions in Euclidean and Hermitean Clifford analysis. ARCHIVUM MATHEMATICUM. 2010;46(5):301–21.
MLA
Brackx, Fred, Hennie De Schepper, and Vladímir Souček. “Fischer Decompositions in Euclidean and Hermitean Clifford Analysis.” ARCHIVUM MATHEMATICUM 46.5 (2010): 301–321. Print.