  We study the orthogonal projection of homogeneous polynomials onto the space
of homogeneous polyharmonic polynomials. To do this we derive the decomposition
of homogeneous polynomials in terms of the Kelvin transform of derivatives of
the fundamental solution $|x|^{2-n}$ or $\log |x|$. We consider also the vector
bases of the space of homogeneous polyharmonic polynomials and study the
problem of convergence of orthogonal series.
