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

被引：0

作者：

Gadzhimirzaev, R. M. ^{[1
]}

机构：

[1] Russian Acad Sci, Dept Math & Comp Sci, Dagestan Fed Res Ctr, Makhachkala 367000, Russia

来源：

MATHEMATICAL NOTES | 2024年 / 115卷 / 3-4期

关键词：

Sobolev-type inner product; Fourier series; Meixner polynomial; approximation property; Lebesgue function; RESPECT;

D O I：

10.1134/S0001434624030027

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 is an element of W-lp rho N(Omega delta)(r) in this system converges to f pointwise on the grid Omega(delta) as p >= 2. In addition, we study the approximation properties of partial sums of Fourier series in the system {m(n,N)(0,r)(x)}.

引用

页码：301 / 316

页数：16

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