# Well-Separated Spherical Designs

@article{Bondarenko2013WellSeparatedSD,
title={Well-Separated Spherical Designs},
author={Andriy V. Bondarenko and Danylo V. Radchenko and Maryna S. Viazovska},
journal={Constructive Approximation},
year={2013},
volume={41},
pages={93-112}
}
• Published 24 March 2013
• Mathematics
• Constructive Approximation
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 $$d$$d.
• T. Stepanyuk
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AbstractFor any set Φ={f1,f2,...,fs} ofC3-functions on the interval [−1, 1], and for any weight functionw(x) satisfyingL1≥w(x)≥L2(1−|x|)β(L1,L2>0, β≥0) and $$\int_{ - 1}^1 {w(x)dx = 1}$$ , we give a