Weighted ℓ_q approximation problems on the ball and on the sphere

2022/01/18 by Jiansong Li, Heping Wang, Li, Jiansong +1
Mathematics · #26D05 #41A17 #41A55 #65D15 #65D32 #Approximation Theory and Sequence Spaces #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical functions and polynomials #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2201.06705

openalex publication_date 2022/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let L_q,μ, 1≤ q(d+2μ)/q, which are order optimal. We also discuss the least squares quadrature induced by an L_2,μ-Marcinkiewicz-Zygmund family, and get the quadrature errors for W_2,μ^r, r>(d+2μ)/2, which are also order optimal. Meanwhile, we give the corresponding the weighted least ℓ_q approximation theorem and the least squares quadrature errors on the sphere.

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