%0 Journal Article
%T A recursive construction of projective cubature formulas and related isometric embeddings
%A Yuri I. Lyubich
%A Oksana A. Shatalova
%J Mathematics
%D 2013
%I arXiv
%X 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 $\ell_{2; K}^m \rightarrow \ell_{p; K}^n$.
%U http://arxiv.org/abs/1310.4562v2