Geodesic
Polynomial functions on the classical projective spaces
Yu. I. Lyubich1 ; O. A. Shatalova1
1 Technion – Israel Institute of Technology Haifa 32000, Israel
Studia Mathematica, Tome 170 (2005) no. 1, pp. 77-87

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $|\langle{x,\cdot }\rangle|^d$.
DOI : 10.4064/sm170-1-4
Keywords: polynomial functions projective space field mathbb mathbb mathbb nbsp mathbb come corresponding sphere via hopf fibration main theorem states every polynomial function phi degree linear combination elementary functions langle cdot rangle

Yu. I. Lyubich 1 ; O. A. Shatalova 1

1 Technion – Israel Institute of Technology Haifa 32000, Israel 
@article{10_4064_sm170_1_4,
     author = {Yu. I. Lyubich and O. A. Shatalova},
     title = {Polynomial functions on the classical projective spaces},
     journal = {Studia Mathematica},
     pages = {77--87},
     publisher = {mathdoc},
     volume = {170},
     number = {1},
     year = {2005},
     doi = {10.4064/sm170-1-4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm170-1-4/}
}
TY  - JOUR
AU  - Yu. I. Lyubich
AU  - O. A. Shatalova
TI  - Polynomial functions on the classical projective spaces
JO  - Studia Mathematica
PY  - 2005
SP  - 77
EP  - 87
VL  - 170
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm170-1-4/
DO  - 10.4064/sm170-1-4
LA  - en
ID  - 10_4064_sm170_1_4
ER  - 
%0 Journal Article
%A Yu. I. Lyubich
%A O. A. Shatalova
%T Polynomial functions on the classical projective spaces
%J Studia Mathematica
%D 2005
%P 77-87
%V 170
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/sm170-1-4/
%R 10.4064/sm170-1-4
%G en
%F 10_4064_sm170_1_4
Yu. I. Lyubich; O. A. Shatalova. Polynomial functions on the classical projective spaces. Studia Mathematica, Tome 170 (2005) no. 1, pp. 77-87. doi: 10.4064/sm170-1-4

Cité par Sources :