-Dirac operator and the Cartan-Kähler theorem
Archivum Mathematicum (2013)
- Volume: 049, Issue: 5, page 333-346
- ISSN: 0044-8753
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topSalač, Tomáš. "$k$-Dirac operator and the Cartan-Kähler theorem." Archivum Mathematicum 049.5 (2013): 333-346. <http://eudml.org/doc/260766>.
@article{Salač2013,
abstract = {We apply the Cartan-Kähler theorem for the k-Dirac operator studied in Clifford analysis and to the parabolic version of this operator. We show that for $k=2$ the tableaux of the first prolongations of these two operators are involutive. This gives us a new characterization of the set of initial conditions for the 2-Dirac operator.},
author = {Salač, Tomáš},
journal = {Archivum Mathematicum},
keywords = {Clifford analysis; parabolic Dirac operator; Cartan-Kähler theorem; Clifford analysis; parabolic Dirac operator; Cartan-Kähler theorem},
language = {eng},
number = {5},
pages = {333-346},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {$k$-Dirac operator and the Cartan-Kähler theorem},
url = {http://eudml.org/doc/260766},
volume = {049},
year = {2013},
}
TY - JOUR
AU - Salač, Tomáš
TI - $k$-Dirac operator and the Cartan-Kähler theorem
JO - Archivum Mathematicum
PY - 2013
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 049
IS - 5
SP - 333
EP - 346
AB - We apply the Cartan-Kähler theorem for the k-Dirac operator studied in Clifford analysis and to the parabolic version of this operator. We show that for $k=2$ the tableaux of the first prolongations of these two operators are involutive. This gives us a new characterization of the set of initial conditions for the 2-Dirac operator.
LA - eng
KW - Clifford analysis; parabolic Dirac operator; Cartan-Kähler theorem; Clifford analysis; parabolic Dirac operator; Cartan-Kähler theorem
UR - http://eudml.org/doc/260766
ER -
References
top- Bryant, R. L., Chern, S. S., Gardner, R. B, Goldschmidt, H. L., Griffits, P. A., Exterior differential systems, Springer Verlag, 1991. (1991)
- Čap, A., Slovák, J., Parabolic Geometries I, Background and General Theory, American Mathematical Society, Providence, 2009. (2009) Zbl1183.53002MR2532439
- Colombo, F., Sabadini, I., Sommen, F., Struppa, D. C., Analysis of Dirac Systems and Computational Algebra, Birkhauser, Boston, 2004. (2004) Zbl1064.30049MR2089988
- Goodman, R., Wallach, N. R., Representations and Invariants of the Classical Groups, Cambridge University Press, 1998. (1998) Zbl0901.22001
- Ivey, T. A., Landsberg, J. M., Cartan for beginners: Differential geometry via moving frames and exterior differential systems, American Mathematical Society, 2003. (2003) Zbl1105.53001MR2003610
- Morimoto, T., 10.3836/tjm/1270130497, Tokyo J. Math. 14 (1) (1991), 165–179. (1991) Zbl0749.17021DOI10.3836/tjm/1270130497
- Sabadini, I., Sommen, F., Struppa, D. C., van Lancker, P., 10.1007/s002090100297, Math. Z. 239 (2) (2002), 293–320. (2002) Zbl1078.30045MR1888226DOI10.1007/s002090100297
- Salač, T., The generalized Dolbeault complexes in Clifford analysis, Ph.D. thesis, MFF UK, MÚUK, Prague, 2012. (2012)
- Salač, T., k-Dirac operator and parabolic geometries.Complex Analysis and Operator Theory, Complex Analysis and Operator Theory, SP Birkhäuser Verlag Basel, 2013. DOI: http://dx.doi.org/10.1007/s11785-013-0292-8 (2013) MR3160805
- Souček, V., Analogues of the Dolbeault complex and the separation of variables, in M. Eastwood, V. Miller, Symmetries and overdetermined systems of partial differential equations. The IMA volumes in Math. and its Appl., Springer, New York, 2007, pp. 537–550. (2007) MR2384731
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