Spherical designs of harmonic index t

@article{Bannai2013SphericalDO,
title={Spherical designs of harmonic index t},
author={Eiichi Bannai and Takayuki Okuda and Makoto Tagami},
journal={J. Approx. Theory},
year={2013},
volume={195},
pages={1-18}
}
• Published 23 August 2013
• Mathematics
• J. Approx. Theory
• Mathematics
• 2014
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• 2015
A finite subset $Y$ on the unit sphere $S^{n-1} \subseteq \mathbb{R}^n$ is called a spherical design of harmonic index $t$, if the following condition is satisfied: $\sum_{\mathbf{x}\in • Mathematics Electron. J. Comb. • 2017 The classification (non-existence) of tight spherical designs of harmonic index 6 and 8, as well as the asymptotic non-existence of Tight spherical designsof harmonic index$2e$for general$e\geq 3$are shown. • Computer Science Des. Codes Cryptogr. • 2020 A linear programming framework for obtaining upper bounds for the potential energy of spherical codes of fixed cardinality and minimum distance is introduced using Hermite interpolation and polynomials are constructed. • Computer Science Designs, Codes and Cryptography • 2020 A linear programming framework for obtaining upper bounds for the potential energy of spherical codes of fixed cardinality and minimum distance is introduced using Hermite interpolation and polynomials are constructed. References SHOWING 1-10 OF 17 REFERENCES • O. Musin • Mathematics J. Comb. Theory, Ser. A • 2009 • Mathematics • 2010 In this paper we prove the conjecture of Korevaar and Meyers: for each$N\ge c_dt^d$there exists a spherical$t$-design in the sphere$S^d$consisting of$N$points, where$c_d\$ is a constant
• Mathematics
• 2005
Cubature formulas and geometrical designs are described in terms of reproducing kernels for Hilbert spaces of functions on the one hand, and Markov operators associated to orthogonal group
Parafree Groups.- The Finitary Andrews-Curtis Conjecture.- Cuts in Kahler Groups.- Algebraic Mapping-Class Groups of Orientable Surfaces with Boundaries.- Solved and Unsolved Problems Around One
• Mathematics
• 2013
For each $$N\ge C_dt^d$$N≥Cdtd, we prove the existence of a well-separated spherical $$t$$t-design in the sphere $$S^d$$Sd consisting of $$N$$N points, where $$C_d$$Cd is a constant depending only on