A recursive construction of projective cubature formulas and related isometric embeddings

Abstract

A recursive construction is presented for the projective cubature formulas of index $p$ on the unit spheres $S(m,K)\subset K^m$ where $K$ is $R$ or $C$, or $H$. This yields a lot of new upper bounds for the minimal number of nodes $n=N_K(m,p)$ in such formulas or, equivalently, for the minimal $n$ such that there exists an isometric embedding ${\ell }_{2;K}^m\to {\ell }_{p;K}^n$.

arXiv comment17 pages. Version 2 fixes several typos in the Tables in Section 5