Real, complex and functional analysis

On the uniform boundedness of Vallée Poussin means in the system of Meixner polynomials

R. M. Gadzhimirzaev

Department of Mathematics and Computer Science, Dagestan Federal Research Center of the RAS, st. M.Gadzhieva, 45, 367032, Makhachkala, Russia

Abstract: Approximation properties of the de la Vallée Poussin means $V_{n+m,N}^\alpha(f,x)$ of Fourier–Meixner sums are studied. In particular, for $an\le m\le bn$ and $n+m\le \lambda N$ the existence of a constant $c(a,b,\alpha,\lambda)$ is established such that $\|V^\alpha_{n+m,N}(f)\|\le c(a,b,\alpha,\lambda)\|f\|$, where $\|f\|$ is the uniform norm of the function $f$ on the grid $\Omega_\delta$.

Keywords: approximation properties, Meixner polynomials, Fourier series, de la Vallée Poussin means.

UDC: 517.521

MSC: 41A10

Received May 14, 2024, published November 1, 2024

DOI: 10.33048/semi.2024.21.065