EXPLICIT FORMULAS FOR THE REPRODUCING KERNELS OF THE SPACE OF HARMONIC POLYNOMIALS IN THE CASE OF CLASSICAL REAL RANK 1

Abstract

We give the explicit formulas of the reproducing kernels of the space of harmonic polynomials of ⊂ in the case of classical real rank 1, which are gener- alizations of the well-known reproducing formulas of classical harmonic polynomials on the unit sphere or any other SO(p)-orbits in C p . These formulas are expressed as integrals on a single orbit, simplifying our previous results that are expressed as double integrals on some family of nilpotent orbits.