Polynomial functions on the classical projective spaces
Volume 170 / 2005
Studia Mathematica 170 (2005), 77-87
MSC: Primary 33C55; Secondary 46B04.
DOI: 10.4064/sm170-1-4
Abstract
The polynomial functions on a projective space over a field ${\mathbb K}={\mathbb R}$, $\mathbb C$ or $\mathbb H$ come from the corresponding sphere via the Hopf fibration. The main theorem states that every polynomial function $\phi(x)$ of degree $d$ is a linear combination of “elementary” functions $|\langle{x,\cdot }\rangle|^d$.
