| Title:
|
Fischer decompositions in Euclidean and Hermitean Clifford analysis (English) |
| Author:
|
Brackx, Fred |
| Author:
|
de Schepper, Hennie |
| Author:
|
Souček, Vladimír |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
46 |
| Issue:
|
5 |
| Year:
|
2010 |
| Pages:
|
301-321 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $\underline{\partial }$. 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 $\underline{\partial }_J$, leading to the system of equations $\underline{\partial } f = 0 = \underline{\partial }_J f$ 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. (English) |
| Keyword:
|
Fischer decomposition |
| Keyword:
|
Clifford analysis |
| MSC:
|
30G35 |
| idZBL:
|
Zbl 1249.30135 |
| idMR:
|
MR2753985 |
| . |
| Date available:
|
2010-12-14T15:02:24Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141385 |
| . |
| Reference:
|
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| Reference:
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