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 system of polynomials $\{m_{n,N}^{\alpha,r}(x)\}$ 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 $p\geqslant 2$. In addition, we study the approximation properties of partial sums of Fourier series in the system $\{m_{n,N}^{0,r}(x)\}$.