Hermite interpolation on Chebyshev nodes and Walsh equiconvergence (Q1970253)

This paper contains in the first part a nice survey of results about Walsh equiconvergence; in particular the quantitative results of Totik and generalizations for different interpolation processes. In the second part the authors recall their own results about Hermite interpolation at the roots of Chebyshev polynomials of the first kind [J. Analysis 6, 91-119 (1998; Zbl 0937.41004)]. The interpolated functions are analytic in certain elliptic regions. There are results about the explicit representation of Hermite interpolants as sums of Chebyshev polynomials and their equiconvergence on ellipses to partial sums of Chebyshev expansions.