Advanced search
2 files | 765.81 KB

Fischer decompositions in Euclidean and Hermitean Clifford analysis

(2010) ARCHIVUM MATHEMATICUM. 46(5). p.301-321
Author
Organization
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.
Keywords
Clifford analysis, Fischer decomposition

Downloads

  • fischer 100831.pdf
    • full text
    • |
    • open access
    • |
    • PDF
    • |
    • 217.41 KB
  • (...).pdf
    • full text
    • |
    • UGent only
    • |
    • PDF
    • |
    • 548.40 KB

Citation

Please use this url to cite or link to this publication:

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.
@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},
}