@article{FILBIR2024101651,
title = {Marcinkiewicz–Zygmund inequalities for scattered and random 
data on the q-sphere},
journal = {Applied and Computational Harmonic Analysis},
volume = {71},
pages = {101651},
year = {2024},
issn = {1063-5203},
doi = {https://doi.org/10.1016/j.acha.2024.101651},
url = {https://www.sciencedirect.com/science/article/pii/S1063520324000289},
author = {Frank Filbir and Ralf Hielscher and Thomas Jahn and Tino Ullrich},
keywords = {Coupon collector problem, Discretization, 
Marcinkiewicz–Zygmund inequality, Random matrix, Riesz–Thorin 
interpolation theorem, Scattered data approximation, Spherical harmonics},
abstract = {The 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 paper, 
we put ourselves on the q-dimensional sphere Sq, and investigate how 
well continuous Lp-norms of polynomials f of maximum degree n on the 
sphere Sq can be discretized by positively weighted Lp-sum of finitely 
many samples, and discuss the distortion between the continuous and 
discrete quantities, the number and distribution of the (deterministic 
or randomly chosen) sample points ξ1,…,ξN on Sq, the dimension q, and 
the degree n of the polynomials.}
}