Convergence of the Fourier Series in Meixner–Sobolev Polynomials and Approximation Properties of Its Partial Sums

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-07-05 DOI:10.1134/s0001434624030027

R. M. Gadzhimirzaev

引用次数: 0

Abstract

We study the convergence of Fourier series in the polynomial system \(\{m_{n,N}^{\alpha,r}(x)\}\) orthonormal in the sense of Sobolev and generated by the system of modified Meixner polynomials. In particular, we show that the Fourier series of \(f\in W^r_{l^p_{\rho_N}(\Omega_\delta)}\) in this system converges to \(f\) pointwise on the grid \(\Omega_\delta\) as \(p\ge2\). In addition, we study the approximation properties of partial sums of Fourier series in the system \(\{m_{n,N}^{0,r}(x)\}\).

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Meixner-Sobolev 多项式中傅里叶级数的收敛性及其部分和的逼近特性

Abstract 我们研究了多项式系统 \(\{m_{n,N}^{/alpha,r}(x)\}\)中傅里叶级数的收敛性，该系统在索博列夫意义上是正交的，由修正的梅克斯纳多项式系统生成。特别是，我们证明了在这个系统中 \(f\in W^r_{l^p_{\rho_N}(\Omega_\delta)}\) 的傅里叶级数在网格 \(\Omega_\delta\)上以 \(p\ge2\)的形式点对点地收敛于 \(f\)。此外，我们还研究了系统 \(\{m_{n,N}^{0,r}(x)\}) 中傅里叶级数部分和的近似性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.