H. R. Malonek

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Information Keywords: Totally regular variables, Appell sequences, hypercomplex differen-tiable functions. Abstract The aim of our contribution is to call attention to the relationship between totally regular variables, introduced by R. Delanghe in 1970, and Appell sequences with respect to the hypercom-plex derivative. Under some natural nor-malization(More)
Information Keywords: Hypercomplex Laguerre derivative, Appell sequences, exponential operators, functions of hypercomplex variables. Abstract In hypercomplex context, we have recently constructed Appell sequences with respect to a generalized Laguerre derivative operator. This construction is based on the use of a basic set of monogenic polynomials which(More)
Let Ω be a G-invariant convex domain in C N including 0, where G is a complex Coxeter group associated with reduced root system R ⊂ R N. We consider holomorphic functions f defined in Ω which are Dunkl polyharmonic, that is, Δ h n f 0 for some integer n. Here Δ h N j1 D 2 j is the complex Dunkl Laplacian, and D j is the complex Dunkl operator attached to(More)
In the recent past one of the main concern of research in the field of Hypercomplex Function Theory in Clifford Algebras was the development of a variety of new tools for a deeper understanding about its true elementary roots in the Function Theory of one Complex Variable. Therefore the study of the space of monogenic (Clifford holomorphic) functions by its(More)