The Uniform Convergence of Fourier Series in a System of the Sobolev Orthogonal Polynomials Associated to Ultraspherical Jacobi Polynomials

We obtain some necessary and sufficient conditions on a parameter that ensure that Fourier series in the Sobolev system of polynomials associated to the ultraspherical Jacobi polynomials converge uniformly on to functions in the Sobolev space , where is the ultraspherical weight.