Optimal asymptotic bounds for spherical designs
@article{Bondarenko2010OptimalAB, title={Optimal asymptotic bounds for spherical designs}, author={Andriy V. Bondarenko and Danylo V. Radchenko and Maryna S. Viazovska}, journal={arXiv: Metric Geometry}, year={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 depending only on $d$.
136 Citations
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We extend to the case of a $d$-dimensional compact connected oriented Riemannian manifold $\mathcal M$ the theorem of A. Bondarenko, D. Radchenko and M. Viazovska on the existence of $L$-designs…
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We find t-designs on compact algebraic manifolds with a number of points comparable to the dimension of the space of polynomials of degree t on the manifold. This generalizes results on the sphere by…
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Upper bounds for the potential energy of spherical designs of cardinality close to the Delsarte–Goethals–Seidel bound are derived by linear programming with use of the Hermite interpolating polynomial of the potential function in suitable nodes.
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We derive upper bounds for the potential energy of spherical designs of cardinality close to the Delsarte–Goethals–Seidel bound. These bounds are obtained by linear programming with use of the…
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Cohn--Conway--Elkies--Kumar [Experiment. Math. (2007)] described that one can construct a family of designs on $S^{2n-1}$ from a design on $\mathbb{CP}^{n-1}$. In this paper, we prove their claim for…
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