In this paper,the L_p-convergence of Grünwald interpolation G_n(f,x)based on the zeros of Jacobi polynomials J^((α,β))_n(x)(-1<α,β<1)is considered.L_p-convergence(0<p<2) of Grünwald interpola...In this paper,the L_p-convergence of Grünwald interpolation G_n(f,x)based on the zeros of Jacobi polynomials J^((α,β))_n(x)(-1<α,β<1)is considered.L_p-convergence(0<p<2) of Grünwald interpolation G_n(f,x)is proved for p·Max(α,β)<1.Moreover, L_p-convergence(p>0)of G_n(f,x)is obtained for-1<α,β≤0.Therefore,the results of [1]and [3-5]are improved.展开更多
文摘In this paper,the L_p-convergence of Grünwald interpolation G_n(f,x)based on the zeros of Jacobi polynomials J^((α,β))_n(x)(-1<α,β<1)is considered.L_p-convergence(0<p<2) of Grünwald interpolation G_n(f,x)is proved for p·Max(α,β)<1.Moreover, L_p-convergence(p>0)of G_n(f,x)is obtained for-1<α,β≤0.Therefore,the results of [1]and [3-5]are improved.
