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arXiv · 1308.5101

Spherical designs of harmonic index t

Eiichi Bannai·Takayuki Okuda·Makoto Tagami
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Abstract

Spherical $t$-design is a finite subset on sphere such that, for any polynomial of degree at most $t$, the average value of the integral on sphere can be replaced by the average value at the finite subset. It is well-known that an equivalent condition of spherical design is given in terms of harmonic polynomials. In this paper, we define a spherical design of harmonic index $t$ from the viewpoint of this equivalent condition, and we give its construction and a Fisher type lower bound on the cardinality. Also we investigate whether there is a spherical design of harmonic index attaining the bound.

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Eiichi Bannai, Takayuki Okuda, Makoto Tagami. 2013-08-23. Spherical designs of harmonic index t. https://arxiv.org/abs/1308.5101

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