Geodesic
$k$-Dirac operator and the Cartan-Kähler theorem
Archivum mathematicum, Tome 49 (2013) no. 5, pp. 333-346.

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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.
DOI : 10.5817/AM2013-5-333
Classification : 53C27, 58A15, 58A17
Keywords: Clifford analysis; parabolic Dirac operator; Cartan-Kähler theorem 
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Salač, Tomáš. $k$-Dirac operator and the Cartan-Kähler theorem. Archivum mathematicum, Tome 49 (2013) no. 5, pp. 333-346. doi : 10.5817/AM2013-5-333. http://geodesic.mathdoc.fr/articles/10.5817/AM2013-5-333/

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