Lagrange interpolation on extended generalized Jacobi nodes

What is it about?

We consider the L^p--convergence of interpolatory processes for nonsmooth functions. Therefore we use generalizations of the well-known Marcinkiewicz--Zygmund inequality for trigonometric polynomials to the case of algebraic polynomials, extending a result of Y. Xu. Particularly, we obtain the order of convergence for certain Lagrange and Quasi--Lagrange interpolatory processes on generalized Jacobi nodes. Our approach enables us also to discuss the influence of additional nodes near the endpoints ±1.

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