Polynomial functions on the classical projective spaces

Volume 170 / 2005

Yu. I. Lyubich, O. A. Shatalova 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 $|\langle{x,\cdot }\rangle|^d$.

Authors

  • Yu. I. LyubichTechnion – Israel Institute of Technology
    Haifa 32000, Israel
    e-mail
  • O. A. ShatalovaTechnion – Israel Institute of Technology
    Haifa 32000, Israel
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image