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

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Applied and Computational Harmonic Analysis Pub Date : 2024-02-29 DOI:10.1016/j.acha.2024.101651

Frank Filbir , Ralf Hielscher , Thomas Jahn , Tino Ullrich

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引用次数: 0

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 $S^{q}$ , and investigate how well continuous $L_{p}$ -norms of polynomials f of maximum degree n on the sphere $S^{q}$ can be discretized by positively weighted $L_{p}$ -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 $ξ_{1}, \dots, ξ_{N}$ on $S^{q}$ , the dimension q, and the degree n of the polynomials.

查看原文本刊更多论文

q 球上分散和随机数据的 Marcinkiewicz-Zygmund 不等式

从有限多个样本中恢复多元函数并估计其积分是现代近似理论的核心任务之一。Marcinkiewicz-Zygmund 不等式为恢复和正交两方面提供了答案。在本文中，我们将自己置于 q 维球面 Sq 上，研究球面 Sq 上最大度数为 n 的多项式 f 的连续 Lp-norms 如何通过有限多个样本的正加权 Lp-sum 离散化，并讨论连续和离散量之间的失真、球面 Sq 上（确定或随机选择的）样本点 ξ1，...，ξN 的数量和分布、维数 q 和多项式的度数 n。

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来源期刊

Applied and Computational Harmonic Analysis 物理-物理：数学物理

CiteScore

5.40

自引率

4.00%

发文量

审稿时长

22.9 weeks

期刊介绍： Applied and Computational Harmonic Analysis (ACHA) is an interdisciplinary journal that publishes high-quality papers in all areas of mathematical sciences related to the applied and computational aspects of harmonic analysis, with special emphasis on innovative theoretical development, methods, and algorithms, for information processing, manipulation, understanding, and so forth. The objectives of the journal are to chronicle the important publications in the rapidly growing field of data representation and analysis, to stimulate research in relevant interdisciplinary areas, and to provide a common link among mathematical, physical, and life scientists, as well as engineers.