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Exact Finite Integral Geometry: Directional Kernels and Spherical Designs
We study when an invariant directional average from integral geometry can be replaced exactly by finitely many directions. For an even continuous kernel $ψ:[-1,1]\to\R$, let $T_ψ$ be the associated zonal convolution operator on the sphere and let $\cB_ψK$ be the corresponding surface-area observable
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