Uniform convergence of Fourier series in the system of Sobolev-orthogonal polynomials associated with Jacobi polynomials

Abstract

Necessary and sufficient conditions are obtained on the exponents $\alpha$ and $\beta$ under which the Fourier series in the Sobolev system of polynomials $\mathcal{P}_r^{\alpha,\beta}$ associated with the Jacobi polynomials converge uniformly on $[-1,1]$ to functions in the Sobolev space $W^r_{L^1_{\rho(\alpha,\beta)}}$, where $\rho(\alpha,\beta)$ is the Jacobi weight. Bibliography: 11 titles.