Orthogonal Appell Bases for Hodge-de Rham Systems in Euclidean Spaces

Abstrakt

Recently the Gelfand-Tsetlin construction of orthogonal bases has been explicitly described for homogeneous polynomial solutions of the Hodge-de Rham systems in the Euclidean space of any dimension. In this paper, we study properties of these bases.

In particular, we show that the bases form the Appell system and the corresponding Taylor series expansions are described.

Klíčová slova

• Hodge-de Rham systems
• generalized Moisil-Theodoresco systems
• Gelfand-Tsetlin basis
• Appell property
• Taylor series