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A recursive construction of projective cubature formulas and related isometric embeddings

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arxiv 1310.4562 v2 pith:W5IG4TGS submitted 2013-10-17 math.FA

Yuri I. Lyubich , Oksana A. Shatalova This is my paper · ORCID
classification math.FA
keywords formulasconstructioncubatureisometricminimalprojectiverecursivebounds
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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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  1. Optimal measures for p-frame energies on spheres

    math.MG 2019-08 accept novelty 8.0 of 10

    Tight designs minimize p-frame energies over all probability measures for p between consecutive even integers, and the 600-cell does so on S3 for p in [8,10].

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