On Spherical Designs of Some Harmonic Indices

[摘要] 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: $\sum_{\mathbf{x}\in Y}f(\mathbf{x})=0$ for all real homogeneous harmonic polynomials $f(x

[学科分类] 离散数学和组合数学

[关键词] Spherical designs of harmonic index;Gegenbauer polynomial;Fisher type lower bound;Tight design;Larman-Rogers-Seidel's theorem;Delsarte's method;Semidefinite prog