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Marcinkiewicz–Zygmund inequalities for scattered and random data on the q-sphere.
Appl. Comput. Harmon. Anal. 71:101651 (2024)
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
ISSN (print) / ISBN
1063-5203
e-ISSN
1096-603X
Quellenangaben
Volume: 71,
Article Number: 101651
Publisher
Academic Press
Publishing Place
San Diego, Calif. [u.a.]
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Biological and Medical Imaging (IBMI)
Grants
German Science Foundation (DFG)
Helmholtz Imaging Platform (HIP)
Helmholtz Imaging Platform (HIP)