On the convergence of Kergin and Hakopian interpolants at Leja sequences for the disk (Q452850)

The author studies Kergin and Hakopian interpolation polynomials at the points of a Leja sequence for the unit disk \(D\) of a sufficiently smooth function \(f\) in a neighbourhood of \(D\) which converges uniformly to \(f\) on \(D\). He proves a formula for the Hakopian interpolation at nodes in general positions in \(R^2\). The proof of convergence results requires a higher level of smoothness. Also, when the interpolated function is in the class \(C^\infty\), he proves that all the derivatives of the interpolation polynomials converge uniformly to the corresponding derivatives of the interpolated function.