A recursive construction of projective cubature formulas and related isometric embeddings

2013/10/17 by Yuri I. Lyubich, Lyubich, Yuri I., Oksana A. Shatalova +1
Mathematics · #46B04 #65D32 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46B04 #msc:65D32

paper · pdf · doi:10.48550/arxiv.1310.4562

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

arxiv created 2014/05/23 · arxiv updated 2014/05/26

Abstract

A recursive construction is presented for the projective cubature formulas of index p on the unit spheres S(m,K)⊂ 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 ℓ_{2; K}^m → ℓ_{p; K}ⁿ.

Related

• Lower bounds for projective designs, cubature formulas and related isometric embeddings
• Construction of spherical cubature formulas using lattices
• Numerical cubature from Archimedes' hat-box theorem
• Canonical isometric embeddings of projective spaces into spheres
• On positive cubature rules on the simplex and isometric embeddings