Orthogonal Appell bases for Hodge-de Rham systems in Euclidean spaces

Details Orthogonal Appell bases for Hodge-de Rham systems in Euclidean spaces Orthogonal Appell bases for Hodge-de Rham systems in Euclidean spaces

2011-11-03

arxiv.org/abs/1111.0974v1

Mathematics

Complex Variables

submitted

Scientific paper

Recently the Gelfand-Tsetlin construction of orthogonal bases has been explicitly described for the spaces of k-homogeneous polynomial solutions of the Hodge-de Rham system in the Euclidean space R^m which take values in the space of s-vectors. In this paper, we give another construction of these bases and, mainly, we show that the bases even form complete orthogonal Appell systems. Moreover, we study the corresponding Taylor series expansions. As an application, we construct quite explicitly orthogonal bases for homogeneous solutions of an arbitrary generalized Moisil-Theodoresco system.

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