A recursive construction of projective cubature formulas and related isometric embeddings
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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 $ell_{2; K}^m ightarrow ell_{p; K}^n$.