Convergence of Fourier Series with Respect to Wihner Polynomials

Classical orthogonal polynomials and their properties are well-known worldwide. In particular, Legendre, Jacob, Lager, Hagenbauer polynomials, and others. With these orthogonal polynomials, are determined the Fourier series and studying the presentation of functions by using these series. They also consider the issues of convergence of these series and summability by different methods. During the study of the convergence and summability of the Fourier series with respect to the system of generalized spherical functions, it is necessary to consider the Fourier series with respect to the Wigner polynomials. Therefore, it is natural to study the convergence and summability of these series. In this paper, the sufficient conditions for the convergence of the Fourier series with respect to the Wigner polynomials are reviewed. In particular, conditions similar to Din's and Jordan's conditions for Fourier's trigonometric series are given, and due these conditions, different signs of convergence for Fourier's series with respect to Wigner's polynomials are proved.