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Filbir, F. ; Hielscher, R.* ; Jahn, T.* ; Ullrich, T.*

Marcinkiewicz–Zygmund inequalities for scattered and random data on the q-sphere.

Appl. Comput. Harmon. Anal. 71:101651 (2024)
Verlagsversion DOI
Open Access Gold (Paid Option)
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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.
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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Korrespondenzautor
Schlagwörter Coupon Collector Problem ; Discretization ; Marcinkiewicz–zygmund Inequality ; Random Matrix ; Riesz–thorin Interpolation Theorem ; Scattered Data Approximation ; Spherical Harmonics; Approximation; Frames
ISSN (print) / ISBN 1063-5203
e-ISSN 1096-603X
Zeitschrift Applied and Computational Harmonic Analysis
Quellenangaben Band: 71, Heft: , Seiten: , Artikelnummer: 101651 Supplement: ,
Verlag Academic Press
Verlagsort San Diego, Calif. [u.a.]
Nichtpatentliteratur Publikationen
Begutachtungsstatus Peer reviewed
Institut(e) Institute of Biological and Medical Imaging (IBMI)
Förderungen German Science Foundation (DFG)
Helmholtz Imaging Platform (HIP)