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}
}
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28 Citations
Highly Influential Citations
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12
Methods Citations
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Results Citations
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28 Citations

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References

SHOWING 1-10 OF 17 REFERENCES

Spherical codes and designs

Spherical two-distance sets

  • O. Musin
  • Mathematics
    J. Comb. Theory, Ser. A
  • 2009

Optimal asymptotic bounds for spherical designs

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…

On Spherical t-designs in ℝ2

A survey on spherical designs and algebraic combinatorics on spheres

Cubature Formulas, Geometrical Designs, Reproducing Kernels, and Markov Operators

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…

On Euclidean Sets Having Only Two Distances Between Points. II

Infinite groups : geometric, combinatorial and dynamical aspects

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…

Well-Separated Spherical Designs

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…

On a special function