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Helmuth R. Malonek

Publications and source records attributed to Helmuth R. Malonek.

4 recordsLinked to original sources
arXiv2014

A unified matrix approach to the representation of Appell polynomials

In this paper we propose a unified approach to matrix representations of different types of Appell polynomials. This approach is based on the creation matrix - a special matrix which has only the natural numbers as entries and is closely related to the well known Pascal matrix. By this means we stress the arithmetical origins of Appell polynomials. The approach also allows to derive, in a simplified way, the properties of Appell polynomials by using only matrix operations.

math.CA↗
arXiv2009

Complex Dunkl operators

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 operators for certain Coxeter groups. These complex Dunkl operators have the commutative property, which makes it possible to establish a corresponding complex analysis of Dunkl operators.

math.CV↗
arXiv2009

Fischer decomposition by inframonogenic functions

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 functions by considering the equation DfD=0. The solutions of this "sandwich" equation, which we call inframonogenic functions, are used to obtain a new Fischer decomposition for homogeneous polynomials in R^m.

math.CV↗