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

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 \(\{m_{n,N}^{0,r}(x)\}\) .