The purpose of this paper is to study the pointwise and almost everywhere convergence of the Cesaro means (C,δ) of Fourier-Jacobi expansions, the main term of the Lebesgue constant of the (C ,8) means for - 1<δ≤...The purpose of this paper is to study the pointwise and almost everywhere convergence of the Cesaro means (C,δ) of Fourier-Jacobi expansions, the main term of the Lebesgue constant of the (C ,8) 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 Cesaro means at the critical index δ = α+1/2 are established.展开更多
文摘The purpose of this paper is to study the pointwise and almost everywhere convergence of the Cesaro means (C,δ) of Fourier-Jacobi expansions, the main term of the Lebesgue constant of the (C ,8) 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 Cesaro means at the critical index δ = α+1/2 are established.
