Isometric embeddings and geometric designs

DOI10.1016/0012-365X(94)00116-ZzbMath0813.05015OpenAlexW2077098613MaRDI QIDQ1344622

J. J. Seidel

Publication date: 1994

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0012-365x(94)00116-z

zbMATH Keywords

Banach spacesspherical designapproximationisometric embeddingscubature formulageometric designsEuclidean \(t\)-design

Mathematics Subject Classification ID

Optimal statistical designs (62K05) Other designs, configurations (05B30) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21)

Related Items (12)

Expressing \((a^ 2+b^ 2+c^ 2+d^ 2)^ 3\) as a sum of 23 sixth powers ⋮ Johan Jacob Seidel ⋮ Some constructions of spherical 5-designs ⋮ Remarks on Hilbert identities, isometric embeddings, and invariant cubature ⋮ Orbits of the hyperoctahedral group as Euclidean designs ⋮ QUANTUM DESIGNS: FOUNDATIONS OF A NONCOMMUTATIVE DESIGN THEORY ⋮ Definitions for spherical designs ⋮ Almost Euclidean planes in \(\ell_p^n\) ⋮ Extremality properties of functions and designs on the torus ⋮ On designs in compact metric spaces and a universal bound on their size ⋮ A minimal design of order 11 on the 3-sphere ⋮ On Euclidean designs

Cites Work

• Isometric embeddings between classical Banach spaces, cubature formulas, and spherical designs
• Averaging sets: A generalization of mean values and spherical designs
• Fisher type inequalities for Euclidean t-designs
• Distances, graphs and designs
• Construction of spherical \(t\)-designs
• New spherical 4-designs
• Spherical codes and designs
• Sums of even powers of real linear forms
• Spherical faraday cage for the case of equal point charges and chebyshev-type quadrature on the sphere
• Waring's Problem
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