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arXiv · 1310.4562

A recursive construction of projective cubature formulas and related isometric embeddings

Yuri I. Lyubich·Oksana A. Shatalova
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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 $\ell_{2; K}^m \rightarrow \ell_{p; K}^n$.

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Yuri I. Lyubich, Oksana A. Shatalova. 2014-05-23. A recursive construction of projective cubature formulas and related isometric embeddings. https://arxiv.org/abs/1310.4562

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