On operators of interpolation with respect to solutions of a Cauchy problem and Lagrange-Jacobi polynomials

摘要

We describe classes of continuous functions for which one has pointwise and uniform convergence of certain Lagrange-type operators (constructed from solutions of a Cauchy problem) and the Lagrange-Jacobi interpolation polynomials L_n(~αn,β_n)(F,cosθ). We also obtain sufficient conditions for the equiconvergence of these interpolation processes.