Sampling, Marcinkiewicz-Zygmund inequalities, approximation, and quadrature rules

被引：17
|
作者：
Groechenig, Karlheinz [1 ]
机构：
[1] Univ Vienna, Fac Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria
来源：
JOURNAL OF APPROXIMATION THEORY | 2020年 / 257卷
基金：
奥地利科学基金会;
关键词：
Marcinkiewicz-Zygmund inequality; Sampling; Sobolev spaces; Least square problem; Quadrature rule; Spectral function; Weyl law; Spectral subspace; NUMERICAL-INTEGRATION; INTERPOLATION; RECONSTRUCTIONS; POLYNOMIALS; DESIGNS; BOUNDS;
D O I：
10.1016/j.jat.2020.105455
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Given a sequence of Marcinkiewicz-Zygmund inequalities in L-2, we derive approximation theorems and quadrature rules. The derivation is completely elementary and requires only the definition of Marcinkiewicz-Zygmund inequality, Sobolev spaces, and the solution of least square problems. (C) 2020 Elsevier Inc. All rights reserved.
引用
收藏
页数：20
相关论文
共 50 条
  • [1] AN ABSTRACT APPROACH TO MARCINKIEWICZ-ZYGMUND INEQUALITIES FOR APPROXIMATION AND QUADRATURE IN MODULATION SPACES
    Ehler, Martin
    Grochenig, Karlheinz
    MATHEMATICS OF COMPUTATION, 2024, 93 (350) : 2885 - 2919
  • [2] Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature
    Mhaskar, HN
    Narcowich, FJ
    Ward, JD
    MATHEMATICS OF COMPUTATION, 2001, 70 (235) : 1113 - 1130
  • [3] Marcinkiewicz-Zygmund inequalities
    Ortega-Cerda, Joaquim
    Saludes, Jordi
    JOURNAL OF APPROXIMATION THEORY, 2007, 145 (02) : 237 - 252
  • [4] Multilinear Marcinkiewicz-Zygmund Inequalities
    Daniel Carando
    Martin Mazzitelli
    Sheldy Ombrosi
    Journal of Fourier Analysis and Applications, 2019, 25 : 51 - 85
  • [5] Multilinear Marcinkiewicz-Zygmund Inequalities
    Carando, Daniel
    Mazzitelli, Martin
    Ombrosi, Sheldy
    JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2019, 25 (01) : 51 - 85
  • [6] Optimal constants in the Marcinkiewicz-Zygmund inequalities
    Ferger, Dietmar
    STATISTICS & PROBABILITY LETTERS, 2014, 84 : 96 - 101
  • [7] EXPONENTIAL ROSENTHAL AND MARCINKIEWICZ-ZYGMUND INEQUALITIES
    Ho, Kwok-Pun
    UFA MATHEMATICAL JOURNAL, 2020, 12 (03): : 97 - 106
  • [8] Probabilistic spherical Marcinkiewicz-Zygmund inequalities
    Boettcher, Albrecht
    Kunis, Stefan
    Potts, Daniel
    JOURNAL OF APPROXIMATION THEORY, 2009, 157 (02) : 113 - 126
  • [9] ON A REFINEMENT OF MARCINKIEWICZ-ZYGMUND TYPE INEQUALITIES
    Kpoo, A.
    TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2020, 26 (04): : 196 - 209
  • [10] Marcinkiewicz-Zygmund inequalities in variable Lebesgue spaces
    Bonich, Marcos
    Carando, Daniel
    Mazzitelli, Martin
    BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 2024, 18 (03)
12345