Explicit Formulae for Monogenic Projections

摘要

Spherical monogenics were studied from the very beginning of Clifford analysis (see [2]) and a lot of theirproperties are well understood. In particular, the monogenic projection nr (i.e., the projection from the space of homogeneouspolynomials of order k to the space of spherical monogenics of order k) plays a key role in many different investigations. Thereis a standard integral formula for the projection (see e.g. [4]). Recently, an explicit differential formula was given ([7, 31) forthe projection, analogous to the classical formula for spherical harmonics. The aim of the article is to describe some otherdifferential formulae useful in further applications.