Article ID Journal Published Year Pages File Type
4606944 Journal of Approximation Theory 2015 18 Pages PDF
Abstract

Spherical tt-design is a finite subset on sphere such that, for any polynomial of degree at most tt, 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 tt 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.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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