Pointwise convergence of Fourier-Jacobi series

The purpose of this paper is to study the pointwise and almost everywhere convergence of the Cesàro means (C,δ) of Fourier-Jacobi expansions, the main term of the Lebesgue constant of the (C,δ) means for −1<δ≤α+1/2 is obtained. With the aid of the generalized translation in terms of Jacobi polynomials, pointwise convergence theorems of the (C,δ) means for δ>α+1/2 and equiconvergence theorems for −1<δ≤α+1/2 are proved. The analogues of the Lebesgue, Salem and Young theorems of the Cesàro means at the critical index δ=α+1/2 are established. Supported by the Natural Science Foundation of Beijing