On convergence and divergence of Fourier expansions associated to Jacobi measure with mass points

Abstract

We prove the failure of a.e. convergence of the Fourier expansion in terms of the orthonormal polynomials with respect to the measure (1 - x)?(1 + x)?dx + M?1 + N?1, where ?t is the delta function at a point t and M > 0; N > 0: Lebesgue norms of Koornwinder's Jacobi-type polynomials are applied to obtain a new proof of necessary conditions for mean convergence. .