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

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 ${\mathcal L}_n^{(\alpha_{n},\beta_{n})}(F,\cos\theta)$. We also obtain sufficient conditions for the equiconvergence of these interpolation processes.