"Recovery of Functions from Random Data on Homogeneous Spaces"Filbir, FrankThe recovery of multivariate functions and estimating their integrals from finitely many samples is one of the central tasks in modern approximation theory. Marcinkiewicz–Zygmund inequalities provide answers to both the recovery and the quadrature aspect. In this talk, we focus on functions defined on compact homogeneous spaces and investigate how well continuous $L^p$ -norms of polynomials $P$ of maximum degree $N$ on these spaces can be discretized by positively weighted $L^p$-sum of finitely many samples. We discuss the distortion between the continuous and discrete quantities, the number and distribution of randomly chosen sample points $\xi_1,\dots ,\xi_M$, and the degree of the polynomials. |
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