Special series in Meixner polynomials and Sobolev orthonormal functions generated by Laguerre functions

The report is devoted to the approximation of discrete functions by partial sums of the Fourier series and a special series in modified Meixner polynomials. The main attention is paid to estimates of the corresponding Lebesgue functions. In addition, a system of functions orthonormal in the sense of Sobolev and generated by a system of Laguerre functions is considered. For this system, recurrent relations are obtained and asymptotic properties are investigated. The question of the convergence of the Fourier series in this system to functions from the Sobolev space is also considered.