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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)
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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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Publication type Article: Journal article
Document type Scientific Article
Keywords Coupon Collector Problem ; Discretization ; Marcinkiewicz–zygmund Inequality ; Random Matrix ; Riesz–thorin Interpolation Theorem ; Scattered Data Approximation ; Spherical Harmonics; Approximation; Frames
Language english
Publication Year 2024
HGF-reported in Year 2024
ISSN (print) / ISBN 1063-5203
e-ISSN 1096-603X
Journal Applied and Computational Harmonic Analysis
Quellenangaben Volume: 71, Issue: , Pages: , Article Number: 101651 Supplement: ,
Publisher Academic Press
Publishing Place San Diego, Calif. [u.a.]
Reviewing status Peer reviewed
Institute(s) Institute of Biological and Medical Imaging (IBMI)
POF-Topic(s) 30205 - Bioengineering and Digital Health
Research field(s) Enabling and Novel Technologies
PSP Element(s) G-505595-001
Grants German Science Foundation (DFG)
Helmholtz Imaging Platform (HIP)
DOI 10.1016/j.acha.2024.101651
WOS ID 001202650000001
Scopus ID 85186713367
Erfassungsdatum 2024-05-08
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