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Title: $k$-Dirac operator and the Cartan-Kähler theorem (English)
Author: Salač, Tomáš
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 49
Issue: 5
Year: 2013
Pages: 333-346
Summary lang: English
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Category: math
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Summary: 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. (English)
Keyword: Clifford analysis
Keyword: parabolic Dirac operator
Keyword: Cartan-Kähler theorem
MSC: 53C27
MSC: 58A15
MSC: 58A17
idZBL: Zbl 06383795
idMR: MR3159332
DOI: 10.5817/AM2013-5-333
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Date available: 2014-01-16T11:21:56Z
Last updated: 2015-03-19
Stable URL: http://hdl.handle.net/10338.dmlcz/143557
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Reference: [8] Salač, T.: The generalized Dolbeault complexes in Clifford analysis.Ph.D. thesis, MFF UK, MÚUK, Prague, 2012.
Reference: [9] 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 MR 3160805
Reference: [10] 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. MR 2384731
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