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math.CV2009★ 1 cited
Complex Dunkl operators
Guangbin Ren, Helmuth R. Malonek
The real theory of the Dunkl operators has been developed very extensively, while there still lacks the corresponding complex theory. In this paper we introduce the complex Dunkl o…
math.CV2009★ 21 cited
A Cauchy-Kowalevski theorem for inframonogenic functions
Helmuth R. Malonek, Dixan Peña Peña, Frank Sommen
In this paper we prove a Cauchy-Kowalevski theorem for the functions satisfying the system DfD=0 (called inframonogenic functions).
math.CV2009★ 2 cited
Fischer decomposition by inframonogenic functions
Helmuth R. Malonek, Dixan Peña Peña, Frank Sommen
Let D denote the Dirac operator in the Euclidean space R^m. In this paper, we present a refinement of the biharmonic functions and at the same time an extension of the monogenic fu…